1 Summary

This analyses comprises (a) descriptive (summary) statistics as well as (b) norm values
All analyses were based on the FMI13 as presented in Kohls, Sauer and Walach (2009):

Kohls, N., Sauer, S., & Walach, H. (2009). Facets of mindfulness – Results of an online study investigating the Freiburg mindfulness inventory. Personality and Individual Differences, 46(2), 224–230. https://doi.org/10.1016/j.paid.2008.10.009

Results are presented for (a) a general factor solution (b) and for the two factor solution, based on the paper of Kohls, Sauer and Walach (2009)
The present norm analyses includes the following norm values: z-values, T values, percentage rank empirical, percentage rank based on a normal distribution
For the descriptive analyses, typical statistics are reproted, ie. mean, sd, range, quartiles, skewness, kurtosis as well as a “0-1-standardized mean”, defined as mean/3 (as 3 is the theoretical upper limit of each score). This statistics is meant to easy comparison.
A number of subgroup results are presented: by sex (female and male), continuous mindfulness training (yes or no), whether intensive mindfulnes retreats have been conducted (yes or noy), whether Vipassana training is practiced (yes or no), age (median split, ie., 49 years)

2 Setup

Load R-Packages and other functions used.

library(easystats)
library(here)
library(tidyverse)
#library(knitr)
library(DataExplorer)
#library(scales)
library(knitr)
library(gt)
library(magrittr)  # extract2
library(lavaan)
library(semPlot)
library(psych)

source("R-code/funs.R")
source("R-code/01-prepare-data.R")

3 Data

3.1 Prepare data

d_w_items <- prepare_FMI_data()

## The following items were matched to the *presence* factor:  ffa_1 ffa_2 ffa_3 ffa_5 ffa_7 ffa_10  
## The following items were matched to the *acceptance* factor:  ffa_4 ffa_6 ffa_8 ffa_9 ffa_11 ffa_12 ffa_14  
## mutating factors to character variables

names(d_w_items)

##  [1] "Nummer"                 "STATUS"                 "Einwilligung"          
##  [4] "Alter"                  "Geschlecht"             "Bildung"               
##  [7] "Haushaltsgrösse"        "Religion"               "Evang"                 
## [10] "Islam"                  "Judentum"               "keineRel"              
## [13] "Andere_Religion"        "feste_Stelle"           "Einkommen"             
## [16] "Kursteilnahme"          "tägl_Übung"             "Achts_regel"           
## [19] "Vip_regel"              "Zen_regel"              "TM_regel"              
## [22] "Kontemp_regel"          "Yoga_regel"             "TaiChi_regel"          
## [25] "ChiGong_regel"          "Tantra_regel"           "Ander_regel"           
## [28] "Anderes"                "Praxisjahre"            "Retreats"              
## [31] "Theorie"                "Presence"               "Acceptance"            
## [34] "Summe"                  "Acceptance13"           "SummeFFA13"            
## [37] "phq_sum"                "fmi13_mean"             "presence_mean"         
## [40] "acceptance13_mean"      "fmi14_mean"             "ffa_1"                 
## [43] "ffa_2"                  "ffa_3"                  "ffa_4"                 
## [46] "ffa_5"                  "ffa_6"                  "ffa_7"                 
## [49] "ffa_8"                  "ffa_9"                  "ffa_10"                
## [52] "ffa_11"                 "ffa_12"                 "ffa_13r"               
## [55] "ffa_14"                 "mindfulness_experience"

3.2 Item labels

item_labels <- 
  read_csv("metadata/FMI-items.csv") |> 
  mutate(item_name = paste0("FFA_", nr))

3.3 Matching items to factors

Presence items:

item_labels |> 
  filter(facet_PAID_2009 == "Presence") |> 
  select(nr) |> 
  extract2(1)

## [1]  1  2  3  5  7 10

Acceptance items:

item_labels |> 
  filter(facet_PAID_2009 == "Acceptance") |> 
  select(nr)|> 
  extract2(1)

## [1]  4  6  8  9 11 12 13 14

4 Describe factors

4.1 Visualization of factor distributions

d_w_items %>% 
  select(ends_with("_mean")) %>% 
  plot_density() + theme_minimal()

## NULL

Alternative visualization, keeping the x-axis constant:

facet_labs <- c(acceptance13_mean = "Acceptance",
                fmi13_mean = "FMI-13R",
                fmi14_mean = "FMI-14",
                presence_mean = "Presence")
  

d_w_items %>% 
  select(ends_with("_mean")) %>% 
  pivot_longer(everything()) %>% 
  ggplot(aes(x = value)) +
  geom_density() +
  facet_wrap(~ name, labeller = as_labeller(facet_labs)) +
  theme_minimal() +
  theme(strip.text = element_text(size = 14),
                axis.text = element_text(size =14)) +
  labs(y = "",
       x = "mean score")

4.2 Descriptive statistics

“Mean01” refers to a 0-1-standardized mean.

d_w_items %>% 
  select(ends_with("_mean")) %>% 
  describe_distribution(iqr = FALSE, range = TRUE, quartiles = TRUE) %>% 
  mutate(Mean01 = Mean/3) %>% 
  mutate(Model = c("FMI-13R", "Presence", "Acceptance", "FMI-14")) |> 
  relocate(Mean01, .after = Mean) %>% 
  relocate(Model, .before = everything()) |> 
  select(-Variable, -n_Missing) |> 
  knitr::kable(digits = 2)

Model	Mean	Mean01	SD	Min	Max	Q1	Q3	Skewness	Kurtosis	n
FMI-13R	1.71	0.57	0.51	0.21	3	1.36	2	-0.15	0.16	1012
Presence	1.70	0.57	0.59	0.00	3	1.33	2	-0.24	0.19	1012
Acceptance	1.73	0.58	0.58	0.00	3	1.43	2	-0.22	0.27	1012
FMI-14	1.71	0.57	0.51	0.21	3	1.36	2	-0.15	0.16	1012

4.3 Norms

d_w_items %>% 
  select(ends_with("_mean")) %>% 
  map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                     digits = 2))

$fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.37	1.00	16.35	0.00
0.1	0.00	-3.17	1.00	18.31	0.00
0.2	0.00	-2.97	1.00	20.28	0.00
0.3	0.01	-2.78	1.00	22.24	0.00
0.4	0.01	-2.58	1.00	24.21	0.00
0.5	0.02	-2.38	1.00	26.17	0.01
0.6	0.02	-2.19	1.00	28.13	0.01
0.7	0.03	-1.99	1.02	30.10	0.02
0.8	0.04	-1.79	1.41	32.06	0.04
0.9	0.05	-1.60	1.80	34.02	0.06
1.0	0.09	-1.40	2.20	35.99	0.08
1.1	0.12	-1.20	2.59	37.95	0.11
1.2	0.15	-1.01	2.98	39.92	0.16
1.3	0.21	-0.81	3.38	41.88	0.21
1.4	0.25	-0.62	3.77	43.84	0.27
1.5	0.34	-0.42	4.16	45.81	0.34
1.6	0.40	-0.22	4.55	47.77	0.41
1.7	0.45	-0.03	4.95	49.74	0.49
1.8	0.58	0.17	5.34	51.70	0.57
1.9	0.64	0.37	5.73	53.66	0.64
2.0	0.76	0.56	6.13	55.63	0.71
2.1	0.80	0.76	6.52	57.59	0.78
2.2	0.83	0.96	6.91	59.56	0.83
2.3	0.89	1.15	7.30	61.52	0.88
2.4	0.91	1.35	7.70	63.48	0.91
2.5	0.95	1.54	8.09	65.45	0.94
2.6	0.96	1.74	8.48	67.41	0.96
2.7	0.97	1.94	8.88	69.38	0.97
2.8	0.99	2.13	9.00	71.34	0.98
2.9	0.99	2.33	9.00	73.30	0.99
3.0	1.00	2.53	9.00	75.27	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.86	1.00	21.37	0.00
0.1	0.01	-2.69	1.00	23.06	0.00
0.2	0.02	-2.53	1.00	24.74	0.01
0.3	0.02	-2.36	1.00	26.43	0.01
0.4	0.02	-2.19	1.00	28.12	0.01
0.5	0.04	-2.02	1.00	29.80	0.02
0.6	0.04	-1.85	1.30	31.49	0.03
0.7	0.06	-1.68	1.64	33.18	0.05
0.8	0.06	-1.51	1.97	34.86	0.07
0.9	0.09	-1.34	2.31	36.55	0.09
1.0	0.15	-1.18	2.65	38.24	0.12
1.1	0.15	-1.01	2.98	39.92	0.16
1.2	0.21	-0.84	3.32	41.61	0.20
1.3	0.21	-0.67	3.66	43.30	0.25
1.4	0.29	-0.50	4.00	44.99	0.31
1.5	0.40	-0.33	4.33	46.67	0.37
1.6	0.40	-0.16	4.67	48.36	0.43
1.7	0.52	0.00	5.01	50.05	0.50
1.8	0.52	0.17	5.35	51.73	0.57
1.9	0.64	0.34	5.68	53.42	0.63
2.0	0.77	0.51	6.02	55.11	0.70
2.1	0.77	0.68	6.36	56.79	0.75
2.2	0.84	0.85	6.70	58.48	0.80
2.3	0.84	1.02	7.03	60.17	0.85
2.4	0.89	1.19	7.37	61.85	0.88
2.5	0.93	1.35	7.71	63.54	0.91
2.6	0.93	1.52	8.05	65.23	0.94
2.7	0.96	1.69	8.38	66.91	0.95
2.8	0.96	1.86	8.72	68.60	0.97
2.9	0.98	2.03	9.00	70.29	0.98
3.0	1.00	2.20	9.00	71.97	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.99	1.00	20.06	0.00
0.1	0.01	-2.82	1.00	21.78	0.00
0.2	0.01	-2.65	1.00	23.51	0.00
0.3	0.02	-2.48	1.00	25.24	0.01
0.4	0.02	-2.30	1.00	26.96	0.01
0.5	0.03	-2.13	1.00	28.69	0.02
0.6	0.04	-1.96	1.08	30.42	0.03
0.7	0.04	-1.79	1.43	32.14	0.04
0.8	0.05	-1.61	1.77	33.87	0.05
0.9	0.08	-1.44	2.12	35.60	0.07
1.0	0.13	-1.27	2.47	37.33	0.10
1.1	0.13	-1.09	2.81	39.05	0.14
1.2	0.17	-0.92	3.16	40.78	0.18
1.3	0.24	-0.75	3.50	42.51	0.23
1.4	0.24	-0.58	3.85	44.23	0.28
1.5	0.33	-0.40	4.19	45.96	0.34
1.6	0.42	-0.23	4.54	47.69	0.41
1.7	0.42	-0.06	4.88	49.41	0.48
1.8	0.51	0.11	5.23	51.14	0.55
1.9	0.63	0.29	5.57	52.87	0.61
2.0	0.75	0.46	5.92	54.60	0.68
2.1	0.75	0.63	6.26	56.32	0.74
2.2	0.82	0.80	6.61	58.05	0.79
2.3	0.87	0.98	6.96	59.78	0.84
2.4	0.87	1.15	7.30	61.50	0.87
2.5	0.90	1.32	7.65	63.23	0.91
2.6	0.94	1.50	7.99	64.96	0.93
2.7	0.94	1.67	8.34	66.68	0.95
2.8	0.96	1.84	8.68	68.41	0.97
2.9	0.98	2.01	9.00	70.14	0.98
3.0	1.00	2.19	9.00	71.87	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.37	1.00	16.35	0.00
0.1	0.00	-3.17	1.00	18.31	0.00
0.2	0.00	-2.97	1.00	20.28	0.00
0.3	0.01	-2.78	1.00	22.24	0.00
0.4	0.01	-2.58	1.00	24.21	0.00
0.5	0.02	-2.38	1.00	26.17	0.01
0.6	0.02	-2.19	1.00	28.13	0.01
0.7	0.03	-1.99	1.02	30.10	0.02
0.8	0.04	-1.79	1.41	32.06	0.04
0.9	0.05	-1.60	1.80	34.02	0.06
1.0	0.09	-1.40	2.20	35.99	0.08
1.1	0.12	-1.20	2.59	37.95	0.11
1.2	0.15	-1.01	2.98	39.92	0.16
1.3	0.21	-0.81	3.38	41.88	0.21
1.4	0.25	-0.62	3.77	43.84	0.27
1.5	0.34	-0.42	4.16	45.81	0.34
1.6	0.40	-0.22	4.55	47.77	0.41
1.7	0.45	-0.03	4.95	49.74	0.49
1.8	0.58	0.17	5.34	51.70	0.57
1.9	0.64	0.37	5.73	53.66	0.64
2.0	0.76	0.56	6.13	55.63	0.71
2.1	0.80	0.76	6.52	57.59	0.78
2.2	0.83	0.96	6.91	59.56	0.83
2.3	0.89	1.15	7.30	61.52	0.88
2.4	0.91	1.35	7.70	63.48	0.91
2.5	0.95	1.54	8.09	65.45	0.94
2.6	0.96	1.74	8.48	67.41	0.96
2.7	0.97	1.94	8.88	69.38	0.97
2.8	0.99	2.13	9.00	71.34	0.98
2.9	0.99	2.33	9.00	73.30	0.99
3.0	1.00	2.53	9.00	75.27	0.99

norms <-
d_w_items %>% 
  select(ends_with("_mean")) %>% 
  map(~ compute_all_norms(., 
                          min_score = 0, 
                          max_score = 3, 
                          by = .1), 
      digits = 2)


p_norm1 <- 
norms %>% 
  pluck(1) %>%
  ggplot(aes(x = score, y = z)) +
  geom_line() +
  scale_y_continuous(breaks = c(-2, 0, 2)) +
  theme(strip.text = element_text(size = 14),
                axis.text = element_text(size =14))


p_norm2 <-
norms %>% 
  pluck(1) %>%
  ggplot(aes(x = score, y = stanine)) +
  geom_line() + 
  scale_y_continuous(breaks = c(1, 5, 9)) +
  theme(strip.text = element_text(size = 14),
                axis.text = element_text(size =14))


p_norm3 <-
norms %>% 
  pluck(1) %>%
  ggplot(aes(x = score, y = perc_rank)) +
  geom_line() +
  labs(y = "Percentage")  +
  scale_y_continuous(breaks = c(0, .5, 1),
                     
                     labels = c("0%", "50%", "100%")) +
  theme(strip.text = element_text(size = 14),
                axis.text = element_text(size =14))


see::plots(p_norm1, p_norm2, p_norm3, tags = TRUE,
           n_rows = 3)

# 
# see::plots(p_norm1, p_norm2, p_norm3, tags = TRUE,
#            n_rows = 3,
#            title =  "FMI-13R mean value (x-axis) vs. different norm values (y-axis)")

5 Item statistics and reliability

5.1 FMI14

Item statistics:

fmi14_desc1 <- 
d_w_items |> 
  select(starts_with("ffa_", ignore.case = FALSE)) |> 
  psych::alpha()

col_names <- c("Nr.", "mean", "*SD*", "*r<sub>it</sub>*", "*r<sub>it</sub> dropped*")

fmi14_desc1[["item.stats"]] |> 
  mutate(nr = 1:14) |> 
  select(nr, mean, sd, r.cor, r.drop) |> 
    kable(col.names = col_names, escape = FALSE, digits = 2, row.names = FALSE)

Nr.	mean	SD	r_it	r_it dropped
1	1.91	0.85	0.53	0.49
2	1.51	0.89	0.50	0.46
3	1.42	0.86	0.49	0.45
4	1.89	0.86	0.62	0.57
5	1.84	0.83	0.67	0.63
6	1.80	0.82	0.65	0.60
7	1.78	0.84	0.68	0.63
8	1.84	0.77	0.53	0.49
9	1.71	0.84	0.66	0.61
10	1.72	0.85	0.67	0.62
11	1.74	0.84	0.68	0.64
12	1.54	0.86	0.66	0.61
13	1.67	0.90	0.01	0.00
14	1.60	0.84	0.55	0.51

Omega:

fmi14_omega <- 
d_w_items |> 
  select(starts_with("ffa_", ignore.case = FALSE)) |> 
  psych::omega(nfactors = 1)

fmi14_omega

## Omega 
## Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip, 
##     digits = digits, title = title, sl = sl, labels = labels, 
##     plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option, 
##     covar = covar)
## Alpha:                 0.87 
## G.6:                   0.87 
## Omega Hierarchical:    0.87 
## Omega H asymptotic:    1 
## Omega Total            0.87 
## 
## Schmid Leiman Factor loadings greater than  0.2 
##            g  F1*   h2   h2   u2 p2 com
## ffa_1   0.53      0.28 0.28 0.72  1   1
## ffa_2   0.51      0.26 0.26 0.74  1   1
## ffa_3   0.49      0.24 0.24 0.76  1   1
## ffa_4   0.61      0.37 0.37 0.63  1   1
## ffa_5   0.67      0.45 0.45 0.55  1   1
## ffa_6   0.65      0.43 0.43 0.57  1   1
## ffa_7   0.69      0.47 0.47 0.53  1   1
## ffa_8   0.53      0.28 0.28 0.72  1   1
## ffa_9   0.65      0.42 0.42 0.58  1   1
## ffa_10  0.67      0.45 0.45 0.55  1   1
## ffa_11  0.67      0.45 0.45 0.55  1   1
## ffa_12  0.66      0.43 0.43 0.57  1   1
## ffa_13r                0.00 1.00  1   1
## ffa_14  0.56      0.31 0.31 0.69  1   1
## 
## With Sums of squares  of:
##   g F1*  h2 
## 4.9 0.0 1.9 
## 
## general/max  2.55   max/min =   1.939515e+16
## mean percent general =  1    with sd =  0 and cv of  0 
## Explained Common Variance of the general factor =  1 
## 
## The degrees of freedom are 77  and the fit is  0.4 
## The number of observations was  1012  with Chi Square =  402.03  with prob <  1.7e-45
## The root mean square of the residuals is  0.05 
## The df corrected root mean square of the residuals is  0.05
## RMSEA index =  0.065  and the 10 % confidence intervals are  0.058 0.071
## BIC =  -130.78
## 
## Compare this with the adequacy of just a general factor and no group factors
## The degrees of freedom for just the general factor are 77  and the fit is  0.4 
## The number of observations was  1012  with Chi Square =  402.03  with prob <  1.7e-45
## The root mean square of the residuals is  0.05 
## The df corrected root mean square of the residuals is  0.05 
## 
## RMSEA index =  0.065  and the 10 % confidence intervals are  0.058 0.071
## BIC =  -130.78 
## 
## Measures of factor score adequacy             
##                                                  g F1*
## Correlation of scores with factors            0.94   0
## Multiple R square of scores with factors      0.89   0
## Minimum correlation of factor score estimates 0.78  -1
## 
##  Total, General and Subset omega for each subset
##                                                  g  F1*
## Omega total for total scores and subscales    0.87 0.87
## Omega general for total scores and subscales  0.87 0.87
## Omega group for total scores and subscales    0.00 0.00

5.2 FMI13-R

fmi13_desc1 <- 
d_w_items |> 
  select(starts_with("ffa_", ignore.case = FALSE)) |> 
  select(-ffa_13r) |> 
  psych::alpha()

col_names <- c("Nr.", "mean", "*SD*", "*r<sub>it</sub>*", "*r<sub>it</sub> dropped*")

fmi13_desc1[["item.stats"]] |> 
  mutate(nr = 1:13) |> 
  select(nr, mean, sd, r.cor, r.drop) |> 
    kable(col.names = col_names, escape = FALSE, digits = 2, row.names = FALSE)

Nr.	mean	SD	r_it	r_it dropped
1	1.91	0.85	0.53	0.50
2	1.51	0.89	0.52	0.49
3	1.42	0.86	0.50	0.47
4	1.89	0.86	0.61	0.57
5	1.84	0.83	0.67	0.63
6	1.80	0.82	0.65	0.61
7	1.78	0.84	0.68	0.64
8	1.84	0.77	0.53	0.50
9	1.71	0.84	0.64	0.60
10	1.72	0.85	0.67	0.63
11	1.74	0.84	0.67	0.63
12	1.54	0.86	0.66	0.62
13	1.60	0.84	0.56	0.52

Omega:

fmi13_omega <- 
d_w_items |> 
  select(starts_with("ffa_", ignore.case = FALSE)) |> 
  select(-ffa_13r) |> 
  psych::omega(nfactors = 1)

fmi13_omega

## Omega 
## Call: omegah(m = m, nfactors = nfactors, fm = fm, key = key, flip = flip, 
##     digits = digits, title = title, sl = sl, labels = labels, 
##     plot = plot, n.obs = n.obs, rotate = rotate, Phi = Phi, option = option, 
##     covar = covar)
## Alpha:                 0.88 
## G.6:                   0.88 
## Omega Hierarchical:    0.88 
## Omega H asymptotic:    1 
## Omega Total            0.88 
## 
## Schmid Leiman Factor loadings greater than  0.2 
##           g  F1*   h2   h2   u2 p2 com
## ffa_1  0.53      0.28 0.28 0.72  1   1
## ffa_2  0.51      0.26 0.26 0.74  1   1
## ffa_3  0.49      0.24 0.24 0.76  1   1
## ffa_4  0.61      0.37 0.37 0.63  1   1
## ffa_5  0.67      0.45 0.45 0.55  1   1
## ffa_6  0.65      0.43 0.43 0.57  1   1
## ffa_7  0.69      0.47 0.47 0.53  1   1
## ffa_8  0.53      0.28 0.28 0.72  1   1
## ffa_9  0.65      0.42 0.42 0.58  1   1
## ffa_10 0.67      0.45 0.45 0.55  1   1
## ffa_11 0.67      0.45 0.45 0.55  1   1
## ffa_12 0.66      0.43 0.43 0.57  1   1
## ffa_14 0.56      0.31 0.31 0.69  1   1
## 
## With Sums of squares  of:
##   g F1*  h2 
## 4.9 0.0 1.9 
## 
## general/max  2.55   max/min =   Inf
## mean percent general =  1    with sd =  0 and cv of  0 
## Explained Common Variance of the general factor =  1 
## 
## The degrees of freedom are 65  and the fit is  0.32 
## The number of observations was  1012  with Chi Square =  323.71  with prob <  5.3e-36
## The root mean square of the residuals is  0.04 
## The df corrected root mean square of the residuals is  0.05
## RMSEA index =  0.063  and the 10 % confidence intervals are  0.056 0.07
## BIC =  -126.07
## 
## Compare this with the adequacy of just a general factor and no group factors
## The degrees of freedom for just the general factor are 65  and the fit is  0.32 
## The number of observations was  1012  with Chi Square =  323.71  with prob <  5.3e-36
## The root mean square of the residuals is  0.04 
## The df corrected root mean square of the residuals is  0.05 
## 
## RMSEA index =  0.063  and the 10 % confidence intervals are  0.056 0.07
## BIC =  -126.07 
## 
## Measures of factor score adequacy             
##                                                  g F1*
## Correlation of scores with factors            0.94   0
## Multiple R square of scores with factors      0.89   0
## Minimum correlation of factor score estimates 0.78  -1
## 
##  Total, General and Subset omega for each subset
##                                                  g  F1*
## Omega total for total scores and subscales    0.88 0.88
## Omega general for total scores and subscales  0.88 0.88
## Omega group for total scores and subscales    0.00 0.00

6 CFA

rename the items for the sake of brevity:

fmi_items <- 
 d_w_items %>%
  select(starts_with("ffa"), mindfulness_experience) |> 
  rename_with(~ gsub("^ffa_(\\d+[a-zA-Z]?)$", "i\\1", .), 
              starts_with("ffa_"))

6.1 Setup

cfa_results <- list()

get_results_list <- function(cfa_model, model_name) {
  out <- list()
  
  out <- list(
    obj_name = deparse(substitute(cfa_model)),
    model_name = model_name,
   # overview = list(summary(cfa_model)),
    cfi = fitMeasures(cfa_model)["cfi"],
    tli = fitMeasures(cfa_model)["tli"],
    rmsea = fitMeasures(cfa_model)["rmsea"],
    srmr = fitMeasures(cfa_model)["srmr"]
  )
}

6.1.1 Tetrachoric correlation matrix

polychoric_r <- polychoric(fmi_items |> select(-mindfulness_experience))

polychoric_rho <- polychoric_r$rho

polychoric_rho[lower.tri(polychoric_r$rho, diag = FALSE)] <- NA

polychoric_rho |> kable( digits = 2)

	i1	i2	i3	i4	i5	i6	i7	i8	i9	i10	i11	i12	i13r	i14
i1	1	0.4	0.34	0.35	0.40	0.37	0.48	0.38	0.38	0.40	0.39	0.36	-0.01	0.36
i2	NA	1.0	0.48	0.31	0.44	0.30	0.41	0.32	0.28	0.39	0.35	0.39	-0.15	0.35
i3	NA	NA	1.00	0.30	0.39	0.31	0.40	0.29	0.29	0.41	0.33	0.40	-0.15	0.34
i4	NA	NA	NA	1.00	0.55	0.57	0.47	0.33	0.51	0.43	0.49	0.45	0.09	0.40
i5	NA	NA	NA	NA	1.00	0.53	0.53	0.39	0.43	0.58	0.53	0.46	0.03	0.40
i6	NA	NA	NA	NA	NA	1.00	0.56	0.42	0.51	0.47	0.50	0.47	0.03	0.42
i7	NA	NA	NA	NA	NA	NA	1.00	0.50	0.49	0.51	0.49	0.49	-0.03	0.42
i8	NA	NA	NA	NA	NA	NA	NA	1.00	0.43	0.43	0.41	0.39	-0.04	0.30
i9	NA	NA	NA	NA	NA	NA	NA	NA	1.00	0.54	0.55	0.57	0.11	0.43
i10	NA	NA	NA	NA	NA	NA	NA	NA	NA	1.00	0.56	0.50	0.01	0.40
i11	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	1.00	0.56	0.14	0.43
i12	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	1.00	0.02	0.49
i13r	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	1.00	-0.06
i14	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	NA	1.00

6.2 One general mindfulness factor, including item 13

FMI14 <- 
  "General_Factor=~i1+i2+i3+i4+i5+i6+i7+i8+i9+i10+i11+i12+i13r+i14"

6.2.1 items as categorical, Pearson

one_factor_ordered_pearson <- cfa(FMI14, 
                          data = fmi_items,
                          estimator = "DWLS",
                          ordered = TRUE)

cfa_results[["FMI-14, ordered, Pearson"]] <- 
  get_results_list(one_factor_ordered_pearson,
                   model_name = "FMI-14, ordered, Pearson")

6.2.2 items as categorical, Polychoric

one_factor_ordered_polychoric <- cfa(FMI14, 
                                      data = fmi_items,
                                      estimator = "DWLS",
                                      sample.cov = polychoric_rho,
                                      ordered = TRUE)

cfa_results[["FMI-14, ordered, polychoric"]] <- 
  get_results_list(one_factor_ordered_polychoric,
                   model_name = "FMI-14, ordered, polychoric")

6.2.3 items as numerical

one_factor_numeric <- cfa(FMI14, data = fmi_items)

  cfa_results[["FMI-14, numeric"]] <- 
  get_results_list(one_factor_numeric,
                   model_name = "FMI-14, numeric")

6.2.4 items as categorical, Polychoric, mindfulness practitioners only

one_factor_ordered_polychoric_practitioners <- cfa(FMI14, 
                                     data = fmi_items |> filter(mindfulness_experience == 1),
                                      estimator = "DWLS",
                                      sample.cov = polychoric_rho,
                                      ordered = TRUE)

cfa_results[["FMI-14, ordered, polychoric, mindfulness practitioners"]] <- 
  get_results_list(one_factor_ordered_polychoric_practitioners,
                   model_name = "FMI-14, ordered, polychoric, mindfulness practitioners")

6.3 Two factors (presence, acceptance) without item 13, correlated factors

FMI13R <- "
# Presence:
presence =~ i1 + i2 + i3 + i5 + i7 + i10 

acceptance =~ i4 + i6 + i8 + i9 + i11 + i12 + i14

presence ~~ acceptance
"

6.3.1 items as numeric:

two_factors_numeric <- cfa(FMI13R,
                           data = fmi_items)

cfa_results[["FMI-13R, numeric"]] <-
  get_results_list(two_factors_numeric,
                   model_name = "FMI-13R, numeric")

6.3.2 items as categorical, Pearson

model_two_dim_wo_13_ordered <- cfa(FMI13R,
                                   data = fmi_items,
                                   estimator = "DWLS",
                                   ordered = TRUE)


cfa_results[["FMI-13R, ordered, Pearson"]] <-
  get_results_list(model_two_dim_wo_13_ordered,
                   model_name = "FMI-13R, ordered, Pearson")

6.3.3 items as categorical, Polychoric

model_two_dim_wo_13_ordered_poly<- cfa(FMI13R,
                                   data = fmi_items,
                                   estimator = "DWLS",
                                   sample.cov = polychoric_rho,
                                   ordered = TRUE)


cfa_results[["FMI-13R, ordered, polychoric"]] <-
  get_results_list(model_two_dim_wo_13_ordered_poly,
                   "FMI-13R, ordered, polychoric")

6.3.4 Plot

semPaths(model_two_dim_wo_13_ordered_poly,
         what = "path",
         whatLabels = "stand",
         layout = "circle",
        # sizeMan = 3,
         #style = "lisrel",
         residuals = FALSE,
         #fixed = FALSE,
         intercepts = FALSE,
         normalize = FALSE,
         thresholds = F,
         width = 12,
         height = 6,
        # rotation = 2,
        # intAtSide = TRUE,
       #  nCharNodes = 0
)
title("Two factors, ordered, polychoric")

Standardized parameters are shown (loadings, correlations).

6.4 Two correlated factors, individuals with meditation practice only

6.4.1 items as numeric

model_two_dim_wo_13_meditators_only <- 
  cfa(FMI13R,
      data = fmi_items |> filter(mindfulness_experience == 1))


cfa_results[["FMI-13R, numeric, mindfulness practitioners"]] <-
  get_results_list(model_two_dim_wo_13_meditators_only,
                   model_name = "FMI-13R, numeric, mindfulness practitioners")

6.4.2 items as categorical, Pearson

model_two_dim_wo_13_meditators_only_categorical <- 
  cfa(FMI13R,
      estimator = "DWLS",
      ordered = TRUE,
      data = fmi_items |> filter(mindfulness_experience == 1))

cfa_results[["FMI-13R, ordered, Pearson, mindfulness practitioners"]] <-
  get_results_list(model_two_dim_wo_13_meditators_only_categorical,
                   model_name = "FMI-13R, ordered, Pearson, mindfulness practitioners")

6.4.3 items as categorical, polychoric

model_two_dim_wo_13_meditators_only_categorical_poly <- 
  cfa(FMI13R,
      estimator = "DWLS",
      ordered = TRUE,
      data = fmi_items |> filter(mindfulness_experience == 1))

cfa_results[["FMI-13R, ordered, polychoric, mindfulness practitioners"]] <-
  get_results_list(model_two_dim_wo_13_meditators_only_categorical_poly,
                   model_name = "FMI-13R, ordered, polychoric, mindfulness practitioners")

6.5 Results

cfa_results_df <-
  do.call(rbind, lapply(cfa_results, as.data.frame))

cfa_results_df |> 
  select(-obj_name) |> 
  mutate(Nr = 1:nrow(cfa_results_df)) |> 
  rename(Model = model_name,
         CFI = cfi,
         TLI = tli,
         RMSEA = rmsea,
         SRMR = srmr) |> 
  relocate(Nr, .before = everything()) |> 
  kable(digits = 2, row.names = FALSE)

Nr	Model	CFI	TLI	RMSEA	SRMR
1	FMI-14, ordered, Pearson	0.99	0.99	0.06	0.05
2	FMI-14, ordered, polychoric	0.99	0.99	0.06	0.05
3	FMI-14, numeric	0.92	0.91	0.06	0.04
4	FMI-14, ordered, polychoric, mindfulness practitioners	1.00	1.00	0.03	0.04
5	FMI-13R, numeric	0.95	0.94	0.06	0.04
6	FMI-13R, ordered, Pearson	0.99	0.99	0.05	0.04
7	FMI-13R, ordered, polychoric	0.99	0.99	0.05	0.04
8	FMI-13R, numeric, mindfulness practitioners	0.97	0.97	0.04	0.03
9	FMI-13R, ordered, Pearson, mindfulness practitioners	1.00	1.00	0.02	0.04
10	FMI-13R, ordered, polychoric, mindfulness practitioners	1.00	1.00	0.02	0.04

7 Norm values for different subgroups

The following subgroup variables were considered:

subgroup_vars <- c("Geschlecht", "Achts_regel", "Retreats", "Vip_regel", "age_below_md")
subgroup_vars

## [1] "Geschlecht"   "Achts_regel"  "Retreats"     "Vip_regel"    "age_below_md"

7.1 Split by sex

7.1.1 Stats

d_w_items %>% 
  #filter(Geschlecht %in% c("männlich", "weiblich")) %>% 
  mutate(Geschlecht = as.character(Geschlecht)) %>% 
  describe_fmi_stats(
                     var = Geschlecht)

Geschlecht=female
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.73	0.58	0.57	(0.00, 3.00)	1.29, 2.07	-0.09	-0.13	515
fmi13_mean	1.71	0.57	0.51	(0.21, 3.00)	1.36, 2.07	-0.11	-0.27	515
fmi14_mean	1.71	0.57	0.51	(0.21, 3.00)	1.36, 2.07	-0.11	-0.27	515
presence_mean	1.72	0.57	0.58	(0.00, 3.00)	1.33, 2.00	-0.11	-0.10	515

Geschlecht=male
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.74	0.58	0.59	(0.00, 3.00)	1.43, 2.00	-0.34	0.65	495
fmi13_mean	1.71	0.57	0.51	(0.21, 3.00)	1.43, 2.00	-0.19	0.58	495
fmi14_mean	1.71	0.57	0.51	(0.21, 3.00)	1.43, 2.00	-0.19	0.58	495
presence_mean	1.67	0.56	0.60	(0.00, 3.00)	1.33, 2.00	-0.35	0.42	495

Geschlecht=other
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.79	0.60	0.51	(1.43, 2.14)	1.61, 1.96	9.14e-16	-2.00	2
fmi13_mean	1.50	0.50	0.20	(1.36, 1.64)	1.43, 1.57	0.00	-2.00	2
fmi14_mean	1.50	0.50	0.20	(1.36, 1.64)	1.43, 1.57	0.00	-2.00	2
presence_mean	1.33	0.44	0.00	(1.33, 1.33)	1.33, 1.33			2

Plot:

plot_fmi_descriptives(data = d_w_items,
                      var = Geschlecht)

7.1.2 Norms

for (i in unique(d_w_items$Geschlecht)) { 
  cat("Group: ", i, "\n")
  d_w_items %>% 
    filter(Geschlecht == i) %>% 
    select(ends_with("_mean")) %>% 
    map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                       digits = 2))  %>% print()
}

Group: male $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.33	1.00	16.67	0.00
0.1	0.00	-3.14	1.00	18.61	0.00
0.2	0.00	-2.94	1.00	20.56	0.00
0.3	0.01	-2.75	1.00	22.50	0.00
0.4	0.02	-2.55	1.00	24.45	0.01
0.5	0.02	-2.36	1.00	26.40	0.01
0.6	0.03	-2.17	1.00	28.34	0.02
0.7	0.03	-1.97	1.06	30.29	0.02
0.8	0.05	-1.78	1.45	32.23	0.04
0.9	0.05	-1.58	1.84	34.18	0.06
1.0	0.08	-1.39	2.23	36.13	0.08
1.1	0.12	-1.19	2.61	38.07	0.12
1.2	0.15	-1.00	3.00	40.02	0.16
1.3	0.19	-0.80	3.39	41.96	0.21
1.4	0.23	-0.61	3.78	43.91	0.27
1.5	0.33	-0.41	4.17	45.86	0.34
1.6	0.39	-0.22	4.56	47.80	0.41
1.7	0.46	-0.03	4.95	49.75	0.49
1.8	0.59	0.17	5.34	51.69	0.57
1.9	0.65	0.36	5.73	53.64	0.64
2.0	0.77	0.56	6.12	55.58	0.71
2.1	0.81	0.75	6.51	57.53	0.77
2.2	0.84	0.95	6.90	59.48	0.83
2.3	0.90	1.14	7.28	61.42	0.87
2.4	0.91	1.34	7.67	63.37	0.91
2.5	0.94	1.53	8.06	65.31	0.94
2.6	0.96	1.73	8.45	67.26	0.96
2.7	0.96	1.92	8.84	69.21	0.97
2.8	0.98	2.12	9.00	71.15	0.98
2.9	0.98	2.31	9.00	73.10	0.99
3.0	1.00	2.50	9.00	75.04	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.02	-2.77	1.00	22.27	0.00
0.1	0.02	-2.61	1.00	23.92	0.00
0.2	0.03	-2.44	1.00	25.58	0.01
0.3	0.03	-2.28	1.00	27.24	0.01
0.4	0.04	-2.11	1.00	28.90	0.02
0.5	0.05	-1.94	1.11	30.55	0.03
0.6	0.05	-1.78	1.44	32.21	0.04
0.7	0.07	-1.61	1.77	33.87	0.05
0.8	0.07	-1.45	2.11	35.53	0.07
0.9	0.10	-1.28	2.44	37.18	0.10
1.0	0.15	-1.12	2.77	38.84	0.13
1.1	0.15	-0.95	3.10	40.50	0.17
1.2	0.21	-0.78	3.43	42.15	0.22
1.3	0.21	-0.62	3.76	43.81	0.27
1.4	0.29	-0.45	4.09	45.47	0.33
1.5	0.40	-0.29	4.43	47.13	0.39
1.6	0.40	-0.12	4.76	48.78	0.45
1.7	0.53	0.04	5.09	50.44	0.52
1.8	0.53	0.21	5.42	52.10	0.58
1.9	0.65	0.38	5.75	53.76	0.65
2.0	0.78	0.54	6.08	55.41	0.71
2.1	0.78	0.71	6.41	57.07	0.76
2.2	0.86	0.87	6.75	58.73	0.81
2.3	0.86	1.04	7.08	60.38	0.85
2.4	0.90	1.20	7.41	62.04	0.89
2.5	0.94	1.37	7.74	63.70	0.91
2.6	0.94	1.54	8.07	65.36	0.94
2.7	0.96	1.70	8.40	67.01	0.96
2.8	0.96	1.87	8.73	68.67	0.97
2.9	0.97	2.03	9.00	70.33	0.98
3.0	1.00	2.20	9.00	71.99	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.96	1.00	20.4	0.00
0.1	0.01	-2.79	1.00	22.1	0.00
0.2	0.02	-2.62	1.00	23.8	0.00
0.3	0.03	-2.45	1.00	25.5	0.01
0.4	0.03	-2.28	1.00	27.2	0.01
0.5	0.03	-2.11	1.00	28.9	0.02
0.6	0.04	-1.94	1.12	30.6	0.03
0.7	0.04	-1.77	1.46	32.3	0.04
0.8	0.05	-1.60	1.80	34.0	0.05
0.9	0.06	-1.43	2.14	35.7	0.08
1.0	0.12	-1.26	2.48	37.4	0.10
1.1	0.12	-1.09	2.82	39.1	0.14
1.2	0.15	-0.92	3.16	40.8	0.18
1.3	0.22	-0.75	3.50	42.5	0.23
1.4	0.22	-0.58	3.84	44.2	0.28
1.5	0.31	-0.41	4.18	45.9	0.34
1.6	0.41	-0.24	4.52	47.6	0.41
1.7	0.41	-0.07	4.86	49.3	0.47
1.8	0.51	0.10	5.20	51.0	0.54
1.9	0.62	0.27	5.54	52.7	0.61
2.0	0.76	0.44	5.88	54.4	0.67
2.1	0.76	0.61	6.22	56.1	0.73
2.2	0.82	0.78	6.56	57.8	0.78
2.3	0.86	0.95	6.90	59.5	0.83
2.4	0.86	1.12	7.24	61.2	0.87
2.5	0.90	1.29	7.58	62.9	0.90
2.6	0.94	1.46	7.92	64.6	0.93
2.7	0.94	1.63	8.26	66.3	0.95
2.8	0.96	1.80	8.60	68.0	0.96
2.9	0.97	1.97	8.94	69.7	0.98
3.0	1.00	2.14	9.00	71.4	0.98

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.33	1.00	16.67	0.00
0.1	0.00	-3.14	1.00	18.61	0.00
0.2	0.00	-2.94	1.00	20.56	0.00
0.3	0.01	-2.75	1.00	22.50	0.00
0.4	0.02	-2.55	1.00	24.45	0.01
0.5	0.02	-2.36	1.00	26.40	0.01
0.6	0.03	-2.17	1.00	28.34	0.02
0.7	0.03	-1.97	1.06	30.29	0.02
0.8	0.05	-1.78	1.45	32.23	0.04
0.9	0.05	-1.58	1.84	34.18	0.06
1.0	0.08	-1.39	2.23	36.13	0.08
1.1	0.12	-1.19	2.61	38.07	0.12
1.2	0.15	-1.00	3.00	40.02	0.16
1.3	0.19	-0.80	3.39	41.96	0.21
1.4	0.23	-0.61	3.78	43.91	0.27
1.5	0.33	-0.41	4.17	45.86	0.34
1.6	0.39	-0.22	4.56	47.80	0.41
1.7	0.46	-0.03	4.95	49.75	0.49
1.8	0.59	0.17	5.34	51.69	0.57
1.9	0.65	0.36	5.73	53.64	0.64
2.0	0.77	0.56	6.12	55.58	0.71
2.1	0.81	0.75	6.51	57.53	0.77
2.2	0.84	0.95	6.90	59.48	0.83
2.3	0.90	1.14	7.28	61.42	0.87
2.4	0.91	1.34	7.67	63.37	0.91
2.5	0.94	1.53	8.06	65.31	0.94
2.6	0.96	1.73	8.45	67.26	0.96
2.7	0.96	1.92	8.84	69.21	0.97
2.8	0.98	2.12	9.00	71.15	0.98
2.9	0.98	2.31	9.00	73.10	0.99
3.0	1.00	2.50	9.00	75.04	0.99

Group: female $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.10	0.00
0.1	0.00	-3.19	1.00	18.08	0.00
0.2	0.00	-2.99	1.00	20.06	0.00
0.3	0.00	-2.80	1.00	22.03	0.00
0.4	0.00	-2.60	1.00	24.01	0.00
0.5	0.01	-2.40	1.00	25.99	0.01
0.6	0.01	-2.20	1.00	27.96	0.01
0.7	0.02	-2.01	1.00	29.94	0.02
0.8	0.04	-1.81	1.38	31.92	0.04
0.9	0.06	-1.61	1.78	33.89	0.05
1.0	0.10	-1.41	2.17	35.87	0.08
1.1	0.13	-1.22	2.57	37.85	0.11
1.2	0.15	-1.02	2.97	39.83	0.15
1.3	0.23	-0.82	3.36	41.80	0.21
1.4	0.28	-0.62	3.76	43.78	0.27
1.5	0.35	-0.42	4.15	45.76	0.34
1.6	0.40	-0.23	4.55	47.73	0.41
1.7	0.44	-0.03	4.94	49.71	0.49
1.8	0.57	0.17	5.34	51.69	0.57
1.9	0.62	0.37	5.73	53.66	0.64
2.0	0.75	0.56	6.13	55.64	0.71
2.1	0.79	0.76	6.52	57.62	0.78
2.2	0.83	0.96	6.92	59.59	0.83
2.3	0.88	1.16	7.31	61.57	0.88
2.4	0.90	1.35	7.71	63.55	0.91
2.5	0.95	1.55	8.10	65.52	0.94
2.6	0.97	1.75	8.50	67.50	0.96
2.7	0.97	1.95	8.90	69.48	0.97
2.8	1.00	2.15	9.00	71.45	0.98
2.9	1.00	2.34	9.00	73.43	0.99
3.0	1.00	2.54	9.00	75.41	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-2.95	1.00	20.46	0.00
0.1	0.00	-2.78	1.00	22.18	0.00
0.2	0.01	-2.61	1.00	23.89	0.00
0.3	0.01	-2.44	1.00	25.61	0.01
0.4	0.01	-2.27	1.00	27.32	0.01
0.5	0.03	-2.10	1.00	29.04	0.02
0.6	0.03	-1.92	1.15	30.75	0.03
0.7	0.06	-1.75	1.49	32.47	0.04
0.8	0.06	-1.58	1.84	34.19	0.06
0.9	0.09	-1.41	2.18	35.90	0.08
1.0	0.14	-1.24	2.52	37.62	0.11
1.1	0.14	-1.07	2.87	39.33	0.14
1.2	0.20	-0.90	3.21	41.05	0.19
1.3	0.20	-0.72	3.55	42.77	0.23
1.4	0.29	-0.55	3.90	44.48	0.29
1.5	0.39	-0.38	4.24	46.20	0.35
1.6	0.39	-0.21	4.58	47.91	0.42
1.7	0.50	-0.04	4.93	49.63	0.49
1.8	0.50	0.13	5.27	51.34	0.55
1.9	0.63	0.31	5.61	53.06	0.62
2.0	0.76	0.48	5.96	54.78	0.68
2.1	0.76	0.65	6.30	56.49	0.74
2.2	0.82	0.82	6.64	58.21	0.79
2.3	0.82	0.99	6.98	59.92	0.84
2.4	0.88	1.16	7.33	61.64	0.88
2.5	0.93	1.34	7.67	63.35	0.91
2.6	0.93	1.51	8.01	65.07	0.93
2.7	0.95	1.68	8.36	66.79	0.95
2.8	0.95	1.85	8.70	68.50	0.97
2.9	0.98	2.02	9.00	70.22	0.98
3.0	1.00	2.19	9.00	71.93	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.02	1.00	19.77	0.00
0.1	0.00	-2.85	1.00	21.52	0.00
0.2	0.00	-2.67	1.00	23.27	0.00
0.3	0.01	-2.50	1.00	25.02	0.01
0.4	0.01	-2.32	1.00	26.77	0.01
0.5	0.02	-2.15	1.00	28.53	0.02
0.6	0.03	-1.97	1.06	30.28	0.02
0.7	0.03	-1.80	1.41	32.03	0.04
0.8	0.05	-1.62	1.76	33.78	0.05
0.9	0.09	-1.45	2.11	35.53	0.07
1.0	0.14	-1.27	2.46	37.28	0.10
1.1	0.14	-1.10	2.81	39.03	0.14
1.2	0.18	-0.92	3.16	40.78	0.18
1.3	0.26	-0.75	3.51	42.53	0.23
1.4	0.26	-0.57	3.86	44.28	0.28
1.5	0.34	-0.40	4.21	46.03	0.35
1.6	0.42	-0.22	4.56	47.78	0.41
1.7	0.42	-0.05	4.91	49.53	0.48
1.8	0.51	0.13	5.26	51.28	0.55
1.9	0.63	0.30	5.61	53.03	0.62
2.0	0.75	0.48	5.96	54.78	0.68
2.1	0.75	0.65	6.31	56.53	0.74
2.2	0.83	0.83	6.66	58.28	0.80
2.3	0.87	1.00	7.01	60.03	0.84
2.4	0.87	1.18	7.36	61.79	0.88
2.5	0.90	1.35	7.71	63.54	0.91
2.6	0.93	1.53	8.06	65.29	0.94
2.7	0.93	1.70	8.41	67.04	0.96
2.8	0.97	1.88	8.76	68.79	0.97
2.9	0.98	2.05	9.00	70.54	0.98
3.0	1.00	2.23	9.00	72.29	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.10	0.00
0.1	0.00	-3.19	1.00	18.08	0.00
0.2	0.00	-2.99	1.00	20.06	0.00
0.3	0.00	-2.80	1.00	22.03	0.00
0.4	0.00	-2.60	1.00	24.01	0.00
0.5	0.01	-2.40	1.00	25.99	0.01
0.6	0.01	-2.20	1.00	27.96	0.01
0.7	0.02	-2.01	1.00	29.94	0.02
0.8	0.04	-1.81	1.38	31.92	0.04
0.9	0.06	-1.61	1.78	33.89	0.05
1.0	0.10	-1.41	2.17	35.87	0.08
1.1	0.13	-1.22	2.57	37.85	0.11
1.2	0.15	-1.02	2.97	39.83	0.15
1.3	0.23	-0.82	3.36	41.80	0.21
1.4	0.28	-0.62	3.76	43.78	0.27
1.5	0.35	-0.42	4.15	45.76	0.34
1.6	0.40	-0.23	4.55	47.73	0.41
1.7	0.44	-0.03	4.94	49.71	0.49
1.8	0.57	0.17	5.34	51.69	0.57
1.9	0.62	0.37	5.73	53.66	0.64
2.0	0.75	0.56	6.13	55.64	0.71
2.1	0.79	0.76	6.52	57.62	0.78
2.2	0.83	0.96	6.92	59.59	0.83
2.3	0.88	1.16	7.31	61.57	0.88
2.4	0.90	1.35	7.71	63.55	0.91
2.5	0.95	1.55	8.10	65.52	0.94
2.6	0.97	1.75	8.50	67.50	0.96
2.7	0.97	1.95	8.90	69.48	0.97
2.8	1.00	2.15	9.00	71.45	0.98
2.9	1.00	2.34	9.00	73.43	0.99
3.0	1.00	2.54	9.00	75.41	0.99

Group: other $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.0	-7.42	1.00	-24.25	0.00
0.1	0.0	-6.93	1.00	-19.30	0.00
0.2	0.0	-6.43	1.00	-14.35	0.00
0.3	0.0	-5.94	1.00	-9.40	0.00
0.4	0.0	-5.44	1.00	-4.45	0.00
0.5	0.0	-4.95	1.00	0.50	0.00
0.6	0.0	-4.45	1.00	5.45	0.00
0.7	0.0	-3.96	1.00	10.40	0.00
0.8	0.0	-3.46	1.00	15.35	0.00
0.9	0.0	-2.97	1.00	20.30	0.00
1.0	0.0	-2.47	1.00	25.25	0.01
1.1	0.0	-1.98	1.04	30.20	0.02
1.2	0.0	-1.48	2.03	35.15	0.07
1.3	0.0	-0.99	3.02	40.10	0.16
1.4	0.5	-0.49	4.01	45.05	0.31
1.5	0.5	0.00	5.00	50.00	0.50
1.6	0.5	0.49	5.99	54.95	0.69
1.7	1.0	0.99	6.98	59.90	0.84
1.8	1.0	1.48	7.97	64.85	0.93
1.9	1.0	1.98	8.96	69.80	0.98
2.0	1.0	2.47	9.00	74.75	0.99
2.1	1.0	2.97	9.00	79.70	1.00
2.2	1.0	3.46	9.00	84.65	1.00
2.3	1.0	3.96	9.00	89.60	1.00
2.4	1.0	4.45	9.00	94.55	1.00
2.5	1.0	4.95	9.00	99.50	1.00
2.6	1.0	5.44	9.00	104.45	1.00
2.7	1.0	5.94	9.00	109.40	1.00
2.8	1.0	6.43	9.00	114.35	1.00
2.9	1.0	6.93	9.00	119.30	1.00
3.0	1.0	7.42	9.00	124.25	1.00

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0	-Inf	1	-Inf	0
0.1	0	-Inf	1	-Inf	0
0.2	0	-Inf	1	-Inf	0
0.3	0	-Inf	1	-Inf	0
0.4	0	-Inf	1	-Inf	0
0.5	0	-Inf	1	-Inf	0
0.6	0	-Inf	1	-Inf	0
0.7	0	-Inf	1	-Inf	0
0.8	0	-Inf	1	-Inf	0
0.9	0	-Inf	1	-Inf	0
1.0	0	-Inf	1	-Inf	0
1.1	0	-Inf	1	-Inf	0
1.2	0	-Inf	1	-Inf	0
1.3	0	-Inf	1	-Inf	0
1.4	1	Inf	9	Inf	1
1.5	1	Inf	9	Inf	1
1.6	1	Inf	9	Inf	1
1.7	1	Inf	9	Inf	1
1.8	1	Inf	9	Inf	1
1.9	1	Inf	9	Inf	1
2.0	1	Inf	9	Inf	1
2.1	1	Inf	9	Inf	1
2.2	1	Inf	9	Inf	1
2.3	1	Inf	9	Inf	1
2.4	1	Inf	9	Inf	1
2.5	1	Inf	9	Inf	1
2.6	1	Inf	9	Inf	1
2.7	1	Inf	9	Inf	1
2.8	1	Inf	9	Inf	1
2.9	1	Inf	9	Inf	1
3.0	1	Inf	9	Inf	1

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.0	-3.54	1.00	14.64	0.00
0.1	0.0	-3.34	1.00	16.62	0.00
0.2	0.0	-3.14	1.00	18.60	0.00
0.3	0.0	-2.94	1.00	20.58	0.00
0.4	0.0	-2.74	1.00	22.56	0.00
0.5	0.0	-2.55	1.00	24.54	0.01
0.6	0.0	-2.35	1.00	26.52	0.01
0.7	0.0	-2.15	1.00	28.50	0.02
0.8	0.0	-1.95	1.10	30.48	0.03
0.9	0.0	-1.75	1.49	32.46	0.04
1.0	0.0	-1.56	1.89	34.44	0.06
1.1	0.0	-1.36	2.28	36.42	0.09
1.2	0.0	-1.16	2.68	38.40	0.12
1.3	0.0	-0.96	3.08	40.38	0.17
1.4	0.0	-0.76	3.47	42.36	0.22
1.5	0.5	-0.57	3.87	44.34	0.29
1.6	0.5	-0.37	4.26	46.32	0.36
1.7	0.5	-0.17	4.66	48.30	0.43
1.8	0.5	0.03	5.06	50.28	0.51
1.9	0.5	0.23	5.45	52.26	0.59
2.0	0.5	0.42	5.85	54.24	0.66
2.1	0.5	0.62	6.24	56.22	0.73
2.2	1.0	0.82	6.64	58.20	0.79
2.3	1.0	1.02	7.04	60.18	0.85
2.4	1.0	1.22	7.43	62.16	0.89
2.5	1.0	1.41	7.83	64.14	0.92
2.6	1.0	1.61	8.22	66.12	0.95
2.7	1.0	1.81	8.62	68.10	0.96
2.8	1.0	2.01	9.00	70.08	0.98
2.9	1.0	2.21	9.00	72.06	0.99
3.0	1.0	2.40	9.00	74.04	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.0	-7.42	1.00	-24.25	0.00
0.1	0.0	-6.93	1.00	-19.30	0.00
0.2	0.0	-6.43	1.00	-14.35	0.00
0.3	0.0	-5.94	1.00	-9.40	0.00
0.4	0.0	-5.44	1.00	-4.45	0.00
0.5	0.0	-4.95	1.00	0.50	0.00
0.6	0.0	-4.45	1.00	5.45	0.00
0.7	0.0	-3.96	1.00	10.40	0.00
0.8	0.0	-3.46	1.00	15.35	0.00
0.9	0.0	-2.97	1.00	20.30	0.00
1.0	0.0	-2.47	1.00	25.25	0.01
1.1	0.0	-1.98	1.04	30.20	0.02
1.2	0.0	-1.48	2.03	35.15	0.07
1.3	0.0	-0.99	3.02	40.10	0.16
1.4	0.5	-0.49	4.01	45.05	0.31
1.5	0.5	0.00	5.00	50.00	0.50
1.6	0.5	0.49	5.99	54.95	0.69
1.7	1.0	0.99	6.98	59.90	0.84
1.8	1.0	1.48	7.97	64.85	0.93
1.9	1.0	1.98	8.96	69.80	0.98
2.0	1.0	2.47	9.00	74.75	0.99
2.1	1.0	2.97	9.00	79.70	1.00
2.2	1.0	3.46	9.00	84.65	1.00
2.3	1.0	3.96	9.00	89.60	1.00
2.4	1.0	4.45	9.00	94.55	1.00
2.5	1.0	4.95	9.00	99.50	1.00
2.6	1.0	5.44	9.00	104.45	1.00
2.7	1.0	5.94	9.00	109.40	1.00
2.8	1.0	6.43	9.00	114.35	1.00
2.9	1.0	6.93	9.00	119.30	1.00
3.0	1.0	7.42	9.00	124.25	1.00

7.2 Split by continuous mindfulness training

7.2.1 Stats

describe_fmi_stats(data = d_w_items,
                   var = Achts_regel)

Achts_regel=no
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.72	0.57	0.59	(0.00, 3.00)	1.29, 2.00	-0.21	0.18	792
fmi13_mean	1.69	0.56	0.51	(0.21, 3.00)	1.36, 2.00	-0.16	0.05	792
fmi14_mean	1.69	0.56	0.51	(0.21, 3.00)	1.36, 2.00	-0.16	0.05	792
presence_mean	1.65	0.55	0.59	(0.00, 3.00)	1.33, 2.00	-0.23	0.13	792

Achts_regel=yes
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.80	0.60	0.55	(0.00, 3.00)	1.43, 2.14	-0.19	0.64	220
fmi13_mean	1.81	0.60	0.49	(0.21, 3.00)	1.50, 2.07	-0.02	0.52	220
fmi14_mean	1.81	0.60	0.49	(0.21, 3.00)	1.50, 2.07	-0.02	0.52	220
presence_mean	1.86	0.62	0.56	(0.00, 3.00)	1.50, 2.17	-0.20	0.45	220

plot_fmi_descriptives(data = d_w_items,
                      var = Achts_regel)

7.2.2 Norms

for (i in unique(d_w_items$Achts_regel)) { 
  cat("Group: ", i, "\n")
  d_w_items %>% 
    filter(Achts_regel == i) %>% 
    select(ends_with("_mean")) %>% 
    map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                       digits = 2)) %>% print()
}

Group: no $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.29	1.00	17.11	0.00
0.1	0.00	-3.09	1.00	19.06	0.00
0.2	0.00	-2.90	1.00	21.01	0.00
0.3	0.01	-2.70	1.00	22.96	0.00
0.4	0.01	-2.51	1.00	24.91	0.01
0.5	0.02	-2.31	1.00	26.86	0.01
0.6	0.03	-2.12	1.00	28.81	0.02
0.7	0.03	-1.92	1.15	30.76	0.03
0.8	0.05	-1.73	1.54	32.71	0.04
0.9	0.06	-1.53	1.93	34.66	0.06
1.0	0.10	-1.34	2.32	36.61	0.09
1.1	0.13	-1.14	2.71	38.56	0.13
1.2	0.17	-0.95	3.10	40.51	0.17
1.3	0.23	-0.75	3.49	42.46	0.23
1.4	0.27	-0.56	3.88	44.41	0.29
1.5	0.36	-0.36	4.27	46.36	0.36
1.6	0.42	-0.17	4.66	48.31	0.43
1.7	0.48	0.03	5.05	50.26	0.51
1.8	0.60	0.22	5.44	52.21	0.59
1.9	0.65	0.42	5.83	54.16	0.66
2.0	0.78	0.61	6.22	56.11	0.73
2.1	0.81	0.81	6.61	58.06	0.79
2.2	0.84	1.00	7.00	60.01	0.84
2.3	0.90	1.20	7.39	61.97	0.88
2.4	0.91	1.39	7.78	63.92	0.92
2.5	0.95	1.59	8.17	65.87	0.94
2.6	0.97	1.78	8.56	67.82	0.96
2.7	0.97	1.98	8.95	69.77	0.98
2.8	0.99	2.17	9.00	71.72	0.99
2.9	0.99	2.37	9.00	73.67	0.99
3.0	1.00	2.56	9.00	75.62	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.78	1.00	22.18	0.00
0.1	0.01	-2.61	1.00	23.87	0.00
0.2	0.02	-2.44	1.00	25.55	0.01
0.3	0.02	-2.28	1.00	27.23	0.01
0.4	0.03	-2.11	1.00	28.92	0.02
0.5	0.05	-1.94	1.12	30.60	0.03
0.6	0.05	-1.77	1.46	32.28	0.04
0.7	0.07	-1.60	1.79	33.97	0.05
0.8	0.07	-1.44	2.13	35.65	0.08
0.9	0.10	-1.27	2.47	37.33	0.10
1.0	0.16	-1.10	2.80	39.02	0.14
1.1	0.16	-0.93	3.14	40.70	0.18
1.2	0.23	-0.76	3.48	42.38	0.22
1.3	0.23	-0.59	3.81	44.07	0.28
1.4	0.32	-0.43	4.15	45.75	0.34
1.5	0.43	-0.26	4.49	47.43	0.40
1.6	0.43	-0.09	4.82	49.12	0.46
1.7	0.55	0.08	5.16	50.80	0.53
1.8	0.55	0.25	5.50	52.48	0.60
1.9	0.67	0.42	5.83	54.16	0.66
2.0	0.79	0.58	6.17	55.85	0.72
2.1	0.79	0.75	6.51	57.53	0.77
2.2	0.85	0.92	6.84	59.21	0.82
2.3	0.85	1.09	7.18	60.90	0.86
2.4	0.90	1.26	7.52	62.58	0.90
2.5	0.94	1.43	7.85	64.26	0.92
2.6	0.94	1.59	8.19	65.95	0.94
2.7	0.97	1.76	8.53	67.63	0.96
2.8	0.97	1.93	8.86	69.31	0.97
2.9	0.98	2.10	9.00	71.00	0.98
3.0	1.00	2.27	9.00	72.68	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.92	1.00	20.78	0.00
0.1	0.01	-2.75	1.00	22.49	0.00
0.2	0.01	-2.58	1.00	24.19	0.00
0.3	0.02	-2.41	1.00	25.89	0.01
0.4	0.02	-2.24	1.00	27.60	0.01
0.5	0.03	-2.07	1.00	29.30	0.02
0.6	0.04	-1.90	1.20	31.00	0.03
0.7	0.04	-1.73	1.54	32.71	0.04
0.8	0.06	-1.56	1.88	34.41	0.06
0.9	0.09	-1.39	2.22	36.12	0.08
1.0	0.14	-1.22	2.56	37.82	0.11
1.1	0.14	-1.05	2.90	39.52	0.15
1.2	0.18	-0.88	3.25	41.23	0.19
1.3	0.26	-0.71	3.59	42.93	0.24
1.4	0.26	-0.54	3.93	44.63	0.30
1.5	0.34	-0.37	4.27	46.34	0.36
1.6	0.43	-0.20	4.61	48.04	0.42
1.7	0.43	-0.03	4.95	49.74	0.49
1.8	0.53	0.14	5.29	51.45	0.56
1.9	0.64	0.32	5.63	53.15	0.62
2.0	0.76	0.49	5.97	54.86	0.69
2.1	0.76	0.66	6.31	56.56	0.74
2.2	0.82	0.83	6.65	58.26	0.80
2.3	0.87	1.00	6.99	59.97	0.84
2.4	0.87	1.17	7.33	61.67	0.88
2.5	0.90	1.34	7.67	63.37	0.91
2.6	0.94	1.51	8.02	65.08	0.93
2.7	0.94	1.68	8.36	66.78	0.95
2.8	0.96	1.85	8.70	68.48	0.97
2.9	0.98	2.02	9.00	70.19	0.98
3.0	1.00	2.19	9.00	71.89	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.29	1.00	17.11	0.00
0.1	0.00	-3.09	1.00	19.06	0.00
0.2	0.00	-2.90	1.00	21.01	0.00
0.3	0.01	-2.70	1.00	22.96	0.00
0.4	0.01	-2.51	1.00	24.91	0.01
0.5	0.02	-2.31	1.00	26.86	0.01
0.6	0.03	-2.12	1.00	28.81	0.02
0.7	0.03	-1.92	1.15	30.76	0.03
0.8	0.05	-1.73	1.54	32.71	0.04
0.9	0.06	-1.53	1.93	34.66	0.06
1.0	0.10	-1.34	2.32	36.61	0.09
1.1	0.13	-1.14	2.71	38.56	0.13
1.2	0.17	-0.95	3.10	40.51	0.17
1.3	0.23	-0.75	3.49	42.46	0.23
1.4	0.27	-0.56	3.88	44.41	0.29
1.5	0.36	-0.36	4.27	46.36	0.36
1.6	0.42	-0.17	4.66	48.31	0.43
1.7	0.48	0.03	5.05	50.26	0.51
1.8	0.60	0.22	5.44	52.21	0.59
1.9	0.65	0.42	5.83	54.16	0.66
2.0	0.78	0.61	6.22	56.11	0.73
2.1	0.81	0.81	6.61	58.06	0.79
2.2	0.84	1.00	7.00	60.01	0.84
2.3	0.90	1.20	7.39	61.97	0.88
2.4	0.91	1.39	7.78	63.92	0.92
2.5	0.95	1.59	8.17	65.87	0.94
2.6	0.97	1.78	8.56	67.82	0.96
2.7	0.97	1.98	8.95	69.77	0.98
2.8	0.99	2.17	9.00	71.72	0.99
2.9	0.99	2.37	9.00	73.67	0.99
3.0	1.00	2.56	9.00	75.62	0.99

Group: yes $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.73	1.00	12.68	0.00
0.1	0.00	-3.53	1.00	14.74	0.00
0.2	0.00	-3.32	1.00	16.80	0.00
0.3	0.01	-3.11	1.00	18.86	0.00
0.4	0.01	-2.91	1.00	20.92	0.00
0.5	0.01	-2.70	1.00	22.99	0.00
0.6	0.01	-2.50	1.00	25.05	0.01
0.7	0.01	-2.29	1.00	27.11	0.01
0.8	0.02	-2.08	1.00	29.17	0.02
0.9	0.02	-1.88	1.25	31.23	0.03
1.0	0.06	-1.67	1.66	33.29	0.05
1.1	0.08	-1.46	2.07	35.35	0.07
1.2	0.09	-1.26	2.48	37.42	0.10
1.3	0.14	-1.05	2.90	39.48	0.15
1.4	0.19	-0.85	3.31	41.54	0.20
1.5	0.27	-0.64	3.72	43.60	0.26
1.6	0.32	-0.43	4.13	45.66	0.33
1.7	0.37	-0.23	4.54	47.72	0.41
1.8	0.51	-0.02	4.96	49.79	0.49
1.9	0.57	0.18	5.37	51.85	0.57
2.0	0.70	0.39	5.78	53.91	0.65
2.1	0.77	0.60	6.19	55.97	0.72
2.2	0.81	0.80	6.61	58.03	0.79
2.3	0.87	1.01	7.02	60.09	0.84
2.4	0.90	1.22	7.43	62.16	0.89
2.5	0.92	1.42	7.84	64.22	0.92
2.6	0.94	1.63	8.26	66.28	0.95
2.7	0.95	1.83	8.67	68.34	0.97
2.8	0.97	2.04	9.00	70.40	0.98
2.9	0.98	2.25	9.00	72.46	0.99
3.0	1.00	2.45	9.00	74.52	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-3.31	1.00	16.85	0.00
0.1	0.01	-3.14	1.00	18.64	0.00
0.2	0.01	-2.96	1.00	20.42	0.00
0.3	0.01	-2.78	1.00	22.20	0.00
0.4	0.01	-2.60	1.00	23.99	0.00
0.5	0.01	-2.42	1.00	25.77	0.01
0.6	0.01	-2.24	1.00	27.56	0.01
0.7	0.02	-2.07	1.00	29.34	0.02
0.8	0.02	-1.89	1.22	31.12	0.03
0.9	0.05	-1.71	1.58	32.91	0.04
1.0	0.09	-1.53	1.94	34.69	0.06
1.1	0.09	-1.35	2.29	36.47	0.09
1.2	0.12	-1.17	2.65	38.26	0.12
1.3	0.12	-1.00	3.01	40.04	0.16
1.4	0.20	-0.82	3.36	41.82	0.21
1.5	0.29	-0.64	3.72	43.61	0.26
1.6	0.29	-0.46	4.08	45.39	0.32
1.7	0.40	-0.28	4.44	47.18	0.39
1.8	0.40	-0.10	4.79	48.96	0.46
1.9	0.53	0.07	5.15	50.74	0.53
2.0	0.69	0.25	5.51	52.53	0.60
2.1	0.69	0.43	5.86	54.31	0.67
2.2	0.79	0.61	6.22	56.09	0.73
2.3	0.79	0.79	6.58	57.88	0.78
2.4	0.85	0.97	6.93	59.66	0.83
2.5	0.90	1.14	7.29	61.45	0.87
2.6	0.90	1.32	7.65	63.23	0.91
2.7	0.92	1.50	8.00	65.01	0.93
2.8	0.92	1.68	8.36	66.80	0.95
2.9	0.96	1.86	8.72	68.58	0.97
3.0	1.00	2.04	9.00	70.36	0.98

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.30	1.00	16.96	0.00
0.1	0.00	-3.12	1.00	18.80	0.00
0.2	0.01	-2.94	1.00	20.63	0.00
0.3	0.01	-2.75	1.00	22.46	0.00
0.4	0.01	-2.57	1.00	24.30	0.01
0.5	0.02	-2.39	1.00	26.13	0.01
0.6	0.02	-2.20	1.00	27.96	0.01
0.7	0.02	-2.02	1.00	29.80	0.02
0.8	0.03	-1.84	1.33	31.63	0.03
0.9	0.05	-1.65	1.69	33.46	0.05
1.0	0.09	-1.47	2.06	35.30	0.07
1.1	0.09	-1.29	2.43	37.13	0.10
1.2	0.12	-1.10	2.79	38.96	0.13
1.3	0.18	-0.92	3.16	40.80	0.18
1.4	0.18	-0.74	3.53	42.63	0.23
1.5	0.27	-0.55	3.89	44.46	0.29
1.6	0.38	-0.37	4.26	46.30	0.36
1.7	0.38	-0.19	4.63	48.13	0.43
1.8	0.45	0.00	4.99	49.96	0.50
1.9	0.59	0.18	5.36	51.80	0.57
2.0	0.73	0.36	5.73	53.63	0.64
2.1	0.73	0.55	6.09	55.46	0.71
2.2	0.83	0.73	6.46	57.30	0.77
2.3	0.86	0.91	6.83	59.13	0.82
2.4	0.86	1.10	7.19	60.97	0.86
2.5	0.90	1.28	7.56	62.80	0.90
2.6	0.92	1.46	7.93	64.63	0.93
2.7	0.92	1.65	8.29	66.47	0.95
2.8	0.95	1.83	8.66	68.30	0.97
2.9	0.97	2.01	9.00	70.13	0.98
3.0	1.00	2.20	9.00	71.97	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.73	1.00	12.68	0.00
0.1	0.00	-3.53	1.00	14.74	0.00
0.2	0.00	-3.32	1.00	16.80	0.00
0.3	0.01	-3.11	1.00	18.86	0.00
0.4	0.01	-2.91	1.00	20.92	0.00
0.5	0.01	-2.70	1.00	22.99	0.00
0.6	0.01	-2.50	1.00	25.05	0.01
0.7	0.01	-2.29	1.00	27.11	0.01
0.8	0.02	-2.08	1.00	29.17	0.02
0.9	0.02	-1.88	1.25	31.23	0.03
1.0	0.06	-1.67	1.66	33.29	0.05
1.1	0.08	-1.46	2.07	35.35	0.07
1.2	0.09	-1.26	2.48	37.42	0.10
1.3	0.14	-1.05	2.90	39.48	0.15
1.4	0.19	-0.85	3.31	41.54	0.20
1.5	0.27	-0.64	3.72	43.60	0.26
1.6	0.32	-0.43	4.13	45.66	0.33
1.7	0.37	-0.23	4.54	47.72	0.41
1.8	0.51	-0.02	4.96	49.79	0.49
1.9	0.57	0.18	5.37	51.85	0.57
2.0	0.70	0.39	5.78	53.91	0.65
2.1	0.77	0.60	6.19	55.97	0.72
2.2	0.81	0.80	6.61	58.03	0.79
2.3	0.87	1.01	7.02	60.09	0.84
2.4	0.90	1.22	7.43	62.16	0.89
2.5	0.92	1.42	7.84	64.22	0.92
2.6	0.94	1.63	8.26	66.28	0.95
2.7	0.95	1.83	8.67	68.34	0.97
2.8	0.97	2.04	9.00	70.40	0.98
2.9	0.98	2.25	9.00	72.46	0.99
3.0	1.00	2.45	9.00	74.52	0.99

7.3 Split by retreats

7.3.1 Stats

describe_fmi_stats(data = d_w_items,
                   var = Retreats)

Retreats=Multiple retreats per year
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.81	0.60	0.48	(0.71, 3.00)	1.57, 2.04	-0.03	-0.06	116
fmi13_mean	1.82	0.61	0.43	(0.71, 3.00)	1.57, 2.00	0.03	0.32	116
fmi14_mean	1.82	0.61	0.43	(0.71, 3.00)	1.57, 2.00	0.03	0.32	116
presence_mean	1.84	0.61	0.50	(0.33, 3.00)	1.50, 2.04	-0.15	0.28	116

Retreats=Never
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.70	0.57	0.60	(0.00, 3.00)	1.29, 2.00	-0.27	0.21	673
fmi13_mean	1.68	0.56	0.52	(0.21, 3.00)	1.36, 2.00	-0.18	0.10	673
fmi14_mean	1.68	0.56	0.52	(0.21, 3.00)	1.36, 2.00	-0.18	0.10	673
presence_mean	1.64	0.55	0.59	(0.00, 3.00)	1.33, 2.00	-0.28	0.20	673

Retreats=Once a year
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.73	0.58	0.50	(0.71, 3.00)	1.43, 2.00	0.59	0.46	58
fmi13_mean	1.71	0.57	0.45	(0.57, 2.93)	1.43, 1.98	0.30	0.36	58
fmi14_mean	1.71	0.57	0.45	(0.57, 2.93)	1.43, 1.98	0.30	0.36	58
presence_mean	1.68	0.56	0.55	(0.17, 3.00)	1.33, 2.00	0.04	0.25	58

Retreats=Once every couple of years
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.74	0.58	0.53	(0.29, 3.00)	1.43, 2.11	0.14	0.12	86
fmi13_mean	1.71	0.57	0.46	(0.93, 2.93)	1.36, 2.07	0.38	-0.32	86
fmi14_mean	1.71	0.57	0.46	(0.93, 2.93)	1.36, 2.07	0.38	-0.32	86
presence_mean	1.71	0.57	0.59	(0.67, 3.00)	1.33, 2.17	0.20	-0.44	86

Retreats=Rarely
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.93	0.64	0.63	(0.14, 3.00)	1.57, 2.29	-0.38	0.35	79
fmi13_mean	1.89	0.63	0.55	(0.29, 2.79)	1.57, 2.29	-0.51	0.60	79
fmi14_mean	1.89	0.63	0.55	(0.29, 2.79)	1.57, 2.29	-0.51	0.60	79
presence_mean	1.94	0.65	0.68	(0.00, 3.00)	1.50, 2.33	-0.60	0.63	79

plot_fmi_descriptives(data = d_w_items,
                      var = Retreats)

7.3.2 Norms

for (i in unique(d_w_items$Retreats)) { 
  cat("Group: ", i, "\n")
  d_w_items %>% 
    filter(Retreats == i) %>% 
    select(ends_with("_mean")) %>% 
    map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                       digits = 2)) %>% 
    print()
}

Group: Never $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.22	1.00	17.82	0.00
0.1	0.00	-3.03	1.00	19.74	0.00
0.2	0.00	-2.83	1.00	21.66	0.00
0.3	0.01	-2.64	1.00	23.58	0.00
0.4	0.01	-2.45	1.00	25.50	0.01
0.5	0.02	-2.26	1.00	27.42	0.01
0.6	0.03	-2.07	1.00	29.34	0.02
0.7	0.04	-1.87	1.25	31.26	0.03
0.8	0.06	-1.68	1.64	33.18	0.05
0.9	0.07	-1.49	2.02	35.10	0.07
1.0	0.11	-1.30	2.40	37.02	0.10
1.1	0.14	-1.11	2.79	38.94	0.13
1.2	0.17	-0.91	3.17	40.86	0.18
1.3	0.24	-0.72	3.56	42.78	0.24
1.4	0.29	-0.53	3.94	44.70	0.30
1.5	0.36	-0.34	4.32	46.62	0.37
1.6	0.41	-0.15	4.71	48.54	0.44
1.7	0.47	0.05	5.09	50.46	0.52
1.8	0.60	0.24	5.47	52.37	0.59
1.9	0.66	0.43	5.86	54.29	0.67
2.0	0.77	0.62	6.24	56.21	0.73
2.1	0.81	0.81	6.63	58.13	0.79
2.2	0.85	1.01	7.01	60.05	0.84
2.3	0.90	1.20	7.39	61.97	0.88
2.4	0.92	1.39	7.78	63.89	0.92
2.5	0.95	1.58	8.16	65.81	0.94
2.6	0.97	1.77	8.55	67.73	0.96
2.7	0.97	1.97	8.93	69.65	0.98
2.8	0.99	2.16	9.00	71.57	0.98
2.9	0.99	2.35	9.00	73.49	0.99
3.0	1.00	2.54	9.00	75.41	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.78	1.00	22.23	0.00
0.1	0.01	-2.61	1.00	23.91	0.00
0.2	0.02	-2.44	1.00	25.60	0.01
0.3	0.02	-2.27	1.00	27.29	0.01
0.4	0.03	-2.10	1.00	28.98	0.02
0.5	0.05	-1.93	1.13	30.67	0.03
0.6	0.05	-1.76	1.47	32.36	0.04
0.7	0.08	-1.60	1.81	34.05	0.06
0.8	0.08	-1.43	2.15	35.74	0.08
0.9	0.11	-1.26	2.49	37.43	0.10
1.0	0.16	-1.09	2.82	39.12	0.14
1.1	0.16	-0.92	3.16	40.81	0.18
1.2	0.23	-0.75	3.50	42.49	0.23
1.3	0.23	-0.58	3.84	44.18	0.28
1.4	0.32	-0.41	4.17	45.87	0.34
1.5	0.42	-0.24	4.51	47.56	0.40
1.6	0.42	-0.07	4.85	49.25	0.47
1.7	0.55	0.09	5.19	50.94	0.54
1.8	0.55	0.26	5.53	52.63	0.60
1.9	0.68	0.43	5.86	54.32	0.67
2.0	0.80	0.60	6.20	56.01	0.73
2.1	0.80	0.77	6.54	57.70	0.78
2.2	0.86	0.94	6.88	59.38	0.83
2.3	0.86	1.11	7.21	61.07	0.87
2.4	0.91	1.28	7.55	62.76	0.90
2.5	0.95	1.45	7.89	64.45	0.93
2.6	0.95	1.61	8.23	66.14	0.95
2.7	0.97	1.78	8.57	67.83	0.96
2.8	0.97	1.95	8.90	69.52	0.97
2.9	0.98	2.12	9.00	71.21	0.98
3.0	1.00	2.29	9.00	72.90	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.84	1.00	21.61	0.00
0.1	0.01	-2.67	1.00	23.29	0.00
0.2	0.02	-2.50	1.00	24.96	0.01
0.3	0.02	-2.34	1.00	26.63	0.01
0.4	0.02	-2.17	1.00	28.31	0.02
0.5	0.03	-2.00	1.00	29.98	0.02
0.6	0.05	-1.83	1.33	31.65	0.03
0.7	0.05	-1.67	1.67	33.33	0.05
0.8	0.07	-1.50	2.00	35.00	0.07
0.9	0.10	-1.33	2.33	36.67	0.09
1.0	0.15	-1.17	2.67	38.35	0.12
1.1	0.15	-1.00	3.00	40.02	0.16
1.2	0.20	-0.83	3.34	41.69	0.20
1.3	0.27	-0.66	3.67	43.37	0.25
1.4	0.27	-0.50	4.01	45.04	0.31
1.5	0.35	-0.33	4.34	46.72	0.37
1.6	0.43	-0.16	4.68	48.39	0.44
1.7	0.43	0.01	5.01	50.06	0.50
1.8	0.53	0.17	5.35	51.74	0.57
1.9	0.64	0.34	5.68	53.41	0.63
2.0	0.76	0.51	6.02	55.08	0.69
2.1	0.76	0.68	6.35	56.76	0.75
2.2	0.83	0.84	6.69	58.43	0.80
2.3	0.87	1.01	7.02	60.10	0.84
2.4	0.87	1.18	7.36	61.78	0.88
2.5	0.91	1.35	7.69	63.45	0.91
2.6	0.95	1.51	8.03	65.13	0.93
2.7	0.95	1.68	8.36	66.80	0.95
2.8	0.96	1.85	8.69	68.47	0.97
2.9	0.98	2.01	9.00	70.15	0.98
3.0	1.00	2.18	9.00	71.82	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.22	1.00	17.82	0.00
0.1	0.00	-3.03	1.00	19.74	0.00
0.2	0.00	-2.83	1.00	21.66	0.00
0.3	0.01	-2.64	1.00	23.58	0.00
0.4	0.01	-2.45	1.00	25.50	0.01
0.5	0.02	-2.26	1.00	27.42	0.01
0.6	0.03	-2.07	1.00	29.34	0.02
0.7	0.04	-1.87	1.25	31.26	0.03
0.8	0.06	-1.68	1.64	33.18	0.05
0.9	0.07	-1.49	2.02	35.10	0.07
1.0	0.11	-1.30	2.40	37.02	0.10
1.1	0.14	-1.11	2.79	38.94	0.13
1.2	0.17	-0.91	3.17	40.86	0.18
1.3	0.24	-0.72	3.56	42.78	0.24
1.4	0.29	-0.53	3.94	44.70	0.30
1.5	0.36	-0.34	4.32	46.62	0.37
1.6	0.41	-0.15	4.71	48.54	0.44
1.7	0.47	0.05	5.09	50.46	0.52
1.8	0.60	0.24	5.47	52.37	0.59
1.9	0.66	0.43	5.86	54.29	0.67
2.0	0.77	0.62	6.24	56.21	0.73
2.1	0.81	0.81	6.63	58.13	0.79
2.2	0.85	1.01	7.01	60.05	0.84
2.3	0.90	1.20	7.39	61.97	0.88
2.4	0.92	1.39	7.78	63.89	0.92
2.5	0.95	1.58	8.16	65.81	0.94
2.6	0.97	1.77	8.55	67.73	0.96
2.7	0.97	1.97	8.93	69.65	0.98
2.8	0.99	2.16	9.00	71.57	0.98
2.9	0.99	2.35	9.00	73.49	0.99
3.0	1.00	2.54	9.00	75.41	0.99

Group: Once every couple of years $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.67	1.00	13.26	0.00
0.1	0.00	-3.46	1.00	15.41	0.00
0.2	0.00	-3.24	1.00	17.56	0.00
0.3	0.00	-3.03	1.00	19.72	0.00
0.4	0.00	-2.81	1.00	21.87	0.00
0.5	0.00	-2.60	1.00	24.02	0.00
0.6	0.00	-2.38	1.00	26.17	0.01
0.7	0.00	-2.17	1.00	28.32	0.02
0.8	0.00	-1.95	1.09	30.47	0.03
0.9	0.00	-1.74	1.52	32.62	0.04
1.0	0.07	-1.52	1.96	34.78	0.06
1.1	0.09	-1.31	2.39	36.93	0.10
1.2	0.14	-1.09	2.82	39.08	0.14
1.3	0.23	-0.88	3.25	41.23	0.19
1.4	0.28	-0.66	3.68	43.38	0.25
1.5	0.37	-0.45	4.11	45.53	0.33
1.6	0.48	-0.23	4.54	47.68	0.41
1.7	0.51	-0.02	4.97	49.84	0.49
1.8	0.60	0.20	5.40	51.99	0.58
1.9	0.63	0.41	5.83	54.14	0.66
2.0	0.73	0.63	6.26	56.29	0.74
2.1	0.80	0.84	6.69	58.44	0.80
2.2	0.87	1.06	7.12	60.59	0.86
2.3	0.92	1.27	7.55	62.74	0.90
2.4	0.92	1.49	7.98	64.90	0.93
2.5	0.95	1.70	8.41	67.05	0.96
2.6	0.97	1.92	8.84	69.20	0.97
2.7	0.97	2.14	9.00	71.35	0.98
2.8	0.99	2.35	9.00	73.50	0.99
2.9	0.99	2.57	9.00	75.65	0.99
3.0	1.00	2.78	9.00	77.80	1.00

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-2.91	1.00	20.88	0.00
0.1	0.00	-2.74	1.00	22.58	0.00
0.2	0.00	-2.57	1.00	24.29	0.01
0.3	0.00	-2.40	1.00	26.00	0.01
0.4	0.00	-2.23	1.00	27.70	0.01
0.5	0.00	-2.06	1.00	29.41	0.02
0.6	0.00	-1.89	1.22	31.11	0.03
0.7	0.05	-1.72	1.56	32.82	0.04
0.8	0.05	-1.55	1.90	34.52	0.06
0.9	0.10	-1.38	2.25	36.23	0.08
1.0	0.17	-1.21	2.59	37.94	0.11
1.1	0.17	-1.04	2.93	39.64	0.15
1.2	0.22	-0.87	3.27	41.35	0.19
1.3	0.22	-0.69	3.61	43.05	0.24
1.4	0.29	-0.52	3.95	44.76	0.30
1.5	0.45	-0.35	4.29	46.46	0.36
1.6	0.45	-0.18	4.63	48.17	0.43
1.7	0.56	-0.01	4.97	49.87	0.49
1.8	0.56	0.16	5.32	51.58	0.56
1.9	0.63	0.33	5.66	53.29	0.63
2.0	0.72	0.50	6.00	54.99	0.69
2.1	0.72	0.67	6.34	56.70	0.75
2.2	0.81	0.84	6.68	58.40	0.80
2.3	0.81	1.01	7.02	60.11	0.84
2.4	0.92	1.18	7.36	61.81	0.88
2.5	0.93	1.35	7.70	63.52	0.91
2.6	0.93	1.52	8.04	65.22	0.94
2.7	0.93	1.69	8.39	66.93	0.95
2.8	0.93	1.86	8.73	68.64	0.97
2.9	0.97	2.03	9.00	70.34	0.98
3.0	1.00	2.20	9.00	72.05	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.30	1.00	17.03	0.00
0.1	0.00	-3.11	1.00	18.92	0.00
0.2	0.00	-2.92	1.00	20.82	0.00
0.3	0.01	-2.73	1.00	22.71	0.00
0.4	0.01	-2.54	1.00	24.60	0.01
0.5	0.01	-2.35	1.00	26.50	0.01
0.6	0.01	-2.16	1.00	28.39	0.02
0.7	0.01	-1.97	1.06	30.29	0.02
0.8	0.01	-1.78	1.44	32.18	0.04
0.9	0.05	-1.59	1.81	34.07	0.06
1.0	0.12	-1.40	2.19	35.97	0.08
1.1	0.12	-1.21	2.57	37.86	0.11
1.2	0.15	-1.02	2.95	39.76	0.15
1.3	0.21	-0.84	3.33	41.65	0.20
1.4	0.21	-0.65	3.71	43.54	0.26
1.5	0.35	-0.46	4.09	45.44	0.32
1.6	0.45	-0.27	4.47	47.33	0.39
1.7	0.45	-0.08	4.85	49.23	0.47
1.8	0.55	0.11	5.22	51.12	0.54
1.9	0.63	0.30	5.60	53.01	0.62
2.0	0.74	0.49	5.98	54.91	0.69
2.1	0.74	0.68	6.36	56.80	0.75
2.2	0.84	0.87	6.74	58.70	0.81
2.3	0.87	1.06	7.12	60.59	0.86
2.4	0.87	1.25	7.50	62.48	0.89
2.5	0.93	1.44	7.88	64.38	0.92
2.6	0.95	1.63	8.25	66.27	0.95
2.7	0.95	1.82	8.63	68.17	0.97
2.8	0.97	2.01	9.00	70.06	0.98
2.9	0.97	2.20	9.00	71.95	0.99
3.0	1.00	2.38	9.00	73.85	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.67	1.00	13.26	0.00
0.1	0.00	-3.46	1.00	15.41	0.00
0.2	0.00	-3.24	1.00	17.56	0.00
0.3	0.00	-3.03	1.00	19.72	0.00
0.4	0.00	-2.81	1.00	21.87	0.00
0.5	0.00	-2.60	1.00	24.02	0.00
0.6	0.00	-2.38	1.00	26.17	0.01
0.7	0.00	-2.17	1.00	28.32	0.02
0.8	0.00	-1.95	1.09	30.47	0.03
0.9	0.00	-1.74	1.52	32.62	0.04
1.0	0.07	-1.52	1.96	34.78	0.06
1.1	0.09	-1.31	2.39	36.93	0.10
1.2	0.14	-1.09	2.82	39.08	0.14
1.3	0.23	-0.88	3.25	41.23	0.19
1.4	0.28	-0.66	3.68	43.38	0.25
1.5	0.37	-0.45	4.11	45.53	0.33
1.6	0.48	-0.23	4.54	47.68	0.41
1.7	0.51	-0.02	4.97	49.84	0.49
1.8	0.60	0.20	5.40	51.99	0.58
1.9	0.63	0.41	5.83	54.14	0.66
2.0	0.73	0.63	6.26	56.29	0.74
2.1	0.80	0.84	6.69	58.44	0.80
2.2	0.87	1.06	7.12	60.59	0.86
2.3	0.92	1.27	7.55	62.74	0.90
2.4	0.92	1.49	7.98	64.90	0.93
2.5	0.95	1.70	8.41	67.05	0.96
2.6	0.97	1.92	8.84	69.20	0.97
2.7	0.97	2.14	9.00	71.35	0.98
2.8	0.99	2.35	9.00	73.50	0.99
2.9	0.99	2.57	9.00	75.65	0.99
3.0	1.00	2.78	9.00	77.80	1.00

Group: Multiple retreats per year $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-4.22	1.00	7.83	0.00
0.1	0.00	-3.99	1.00	10.15	0.00
0.2	0.00	-3.75	1.00	12.47	0.00
0.3	0.00	-3.52	1.00	14.79	0.00
0.4	0.00	-3.29	1.00	17.11	0.00
0.5	0.00	-3.06	1.00	19.43	0.00
0.6	0.00	-2.82	1.00	21.75	0.00
0.7	0.00	-2.59	1.00	24.07	0.00
0.8	0.02	-2.36	1.00	26.39	0.01
0.9	0.02	-2.13	1.00	28.71	0.02
1.0	0.03	-1.90	1.21	31.04	0.03
1.1	0.07	-1.66	1.67	33.36	0.05
1.2	0.09	-1.43	2.14	35.68	0.08
1.3	0.13	-1.20	2.60	38.00	0.12
1.4	0.16	-0.97	3.06	40.32	0.17
1.5	0.22	-0.74	3.53	42.64	0.23
1.6	0.28	-0.50	3.99	44.96	0.31
1.7	0.34	-0.27	4.46	47.28	0.39
1.8	0.51	-0.04	4.92	49.60	0.48
1.9	0.59	0.19	5.38	51.92	0.58
2.0	0.76	0.42	5.85	54.24	0.66
2.1	0.78	0.66	6.31	56.57	0.74
2.2	0.80	0.89	6.78	58.89	0.81
2.3	0.90	1.12	7.24	61.21	0.87
2.4	0.91	1.35	7.71	63.53	0.91
2.5	0.93	1.58	8.17	65.85	0.94
2.6	0.95	1.82	8.63	68.17	0.97
2.7	0.97	2.05	9.00	70.49	0.98
2.8	0.99	2.28	9.00	72.81	0.99
2.9	0.99	2.51	9.00	75.13	0.99
3.0	1.00	2.75	9.00	77.45	1.00

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.71	1.00	12.89	0.00
0.1	0.00	-3.51	1.00	14.90	0.00
0.2	0.00	-3.31	1.00	16.92	0.00
0.3	0.00	-3.11	1.00	18.93	0.00
0.4	0.01	-2.91	1.00	20.95	0.00
0.5	0.01	-2.70	1.00	22.96	0.00
0.6	0.01	-2.50	1.00	24.98	0.01
0.7	0.02	-2.30	1.00	26.99	0.01
0.8	0.02	-2.10	1.00	29.01	0.02
0.9	0.03	-1.90	1.20	31.02	0.03
1.0	0.08	-1.70	1.61	33.03	0.04
1.1	0.08	-1.50	2.01	35.05	0.07
1.2	0.12	-1.29	2.41	37.06	0.10
1.3	0.12	-1.09	2.82	39.08	0.14
1.4	0.18	-0.89	3.22	41.09	0.19
1.5	0.28	-0.69	3.62	43.11	0.25
1.6	0.28	-0.49	4.02	45.12	0.31
1.7	0.39	-0.29	4.43	47.14	0.39
1.8	0.39	-0.08	4.83	49.15	0.47
1.9	0.52	0.12	5.23	51.17	0.55
2.0	0.75	0.32	5.64	53.18	0.62
2.1	0.75	0.52	6.04	55.20	0.70
2.2	0.84	0.72	6.44	57.21	0.76
2.3	0.84	0.92	6.85	59.23	0.82
2.4	0.86	1.12	7.25	61.24	0.87
2.5	0.92	1.33	7.65	63.26	0.91
2.6	0.92	1.53	8.05	65.27	0.94
2.7	0.97	1.73	8.46	67.29	0.96
2.8	0.97	1.93	8.86	69.30	0.97
2.9	0.98	2.13	9.00	71.32	0.98
3.0	1.00	2.33	9.00	73.33	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.80	1.00	11.98	0.00
0.1	0.00	-3.59	1.00	14.08	0.00
0.2	0.00	-3.38	1.00	16.18	0.00
0.3	0.00	-3.17	1.00	18.27	0.00
0.4	0.00	-2.96	1.00	20.37	0.00
0.5	0.00	-2.75	1.00	22.47	0.00
0.6	0.00	-2.54	1.00	24.57	0.01
0.7	0.00	-2.33	1.00	26.67	0.01
0.8	0.02	-2.12	1.00	28.77	0.02
0.9	0.03	-1.91	1.17	30.87	0.03
1.0	0.09	-1.70	1.59	32.97	0.04
1.1	0.09	-1.49	2.01	35.07	0.07
1.2	0.11	-1.28	2.43	37.16	0.10
1.3	0.18	-1.07	2.85	39.26	0.14
1.4	0.18	-0.86	3.27	41.36	0.19
1.5	0.23	-0.65	3.69	43.46	0.26
1.6	0.33	-0.44	4.11	45.56	0.33
1.7	0.33	-0.23	4.53	47.66	0.41
1.8	0.43	-0.02	4.95	49.76	0.49
1.9	0.60	0.19	5.37	51.86	0.57
2.0	0.75	0.40	5.79	53.95	0.65
2.1	0.75	0.61	6.21	56.05	0.73
2.2	0.84	0.82	6.63	58.15	0.79
2.3	0.88	1.03	7.05	60.25	0.85
2.4	0.88	1.24	7.47	62.35	0.89
2.5	0.91	1.44	7.89	64.45	0.93
2.6	0.93	1.65	8.31	66.55	0.95
2.7	0.93	1.86	8.73	68.65	0.97
2.8	0.99	2.07	9.00	70.75	0.98
2.9	0.99	2.28	9.00	72.84	0.99
3.0	1.00	2.49	9.00	74.94	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-4.22	1.00	7.83	0.00
0.1	0.00	-3.99	1.00	10.15	0.00
0.2	0.00	-3.75	1.00	12.47	0.00
0.3	0.00	-3.52	1.00	14.79	0.00
0.4	0.00	-3.29	1.00	17.11	0.00
0.5	0.00	-3.06	1.00	19.43	0.00
0.6	0.00	-2.82	1.00	21.75	0.00
0.7	0.00	-2.59	1.00	24.07	0.00
0.8	0.02	-2.36	1.00	26.39	0.01
0.9	0.02	-2.13	1.00	28.71	0.02
1.0	0.03	-1.90	1.21	31.04	0.03
1.1	0.07	-1.66	1.67	33.36	0.05
1.2	0.09	-1.43	2.14	35.68	0.08
1.3	0.13	-1.20	2.60	38.00	0.12
1.4	0.16	-0.97	3.06	40.32	0.17
1.5	0.22	-0.74	3.53	42.64	0.23
1.6	0.28	-0.50	3.99	44.96	0.31
1.7	0.34	-0.27	4.46	47.28	0.39
1.8	0.51	-0.04	4.92	49.60	0.48
1.9	0.59	0.19	5.38	51.92	0.58
2.0	0.76	0.42	5.85	54.24	0.66
2.1	0.78	0.66	6.31	56.57	0.74
2.2	0.80	0.89	6.78	58.89	0.81
2.3	0.90	1.12	7.24	61.21	0.87
2.4	0.91	1.35	7.71	63.53	0.91
2.5	0.93	1.58	8.17	65.85	0.94
2.6	0.95	1.82	8.63	68.17	0.97
2.7	0.97	2.05	9.00	70.49	0.98
2.8	0.99	2.28	9.00	72.81	0.99
2.9	0.99	2.51	9.00	75.13	0.99
3.0	1.00	2.75	9.00	77.45	1.00

Group: Rarely $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.42	1.00	15.83	0.00
0.1	0.00	-3.24	1.00	17.64	0.00
0.2	0.00	-3.05	1.00	19.45	0.00
0.3	0.01	-2.87	1.00	21.27	0.00
0.4	0.01	-2.69	1.00	23.08	0.00
0.5	0.04	-2.51	1.00	24.89	0.01
0.6	0.04	-2.33	1.00	26.70	0.01
0.7	0.04	-2.15	1.00	28.52	0.02
0.8	0.05	-1.97	1.07	30.33	0.02
0.9	0.05	-1.79	1.43	32.14	0.04
1.0	0.05	-1.60	1.79	33.95	0.05
1.1	0.08	-1.42	2.15	35.77	0.08
1.2	0.08	-1.24	2.52	37.58	0.11
1.3	0.09	-1.06	2.88	39.39	0.14
1.4	0.13	-0.88	3.24	41.21	0.19
1.5	0.24	-0.70	3.60	43.02	0.24
1.6	0.30	-0.52	3.97	44.83	0.30
1.7	0.35	-0.34	4.33	46.64	0.37
1.8	0.44	-0.15	4.69	48.46	0.44
1.9	0.49	0.03	5.05	50.27	0.51
2.0	0.63	0.21	5.42	52.08	0.58
2.1	0.68	0.39	5.78	53.89	0.65
2.2	0.71	0.57	6.14	55.71	0.72
2.3	0.77	0.75	6.50	57.52	0.77
2.4	0.80	0.93	6.87	59.33	0.82
2.5	0.89	1.11	7.23	61.14	0.87
2.6	0.90	1.30	7.59	62.96	0.90
2.7	0.90	1.48	7.95	64.77	0.93
2.8	1.00	1.66	8.32	66.58	0.95
2.9	1.00	1.84	8.68	68.40	0.97
3.0	1.00	2.02	9.00	70.21	0.98

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.03	-2.85	1.00	21.48	0.00
0.1	0.03	-2.71	1.00	22.95	0.00
0.2	0.04	-2.56	1.00	24.42	0.01
0.3	0.04	-2.41	1.00	25.90	0.01
0.4	0.04	-2.26	1.00	27.37	0.01
0.5	0.04	-2.12	1.00	28.84	0.02
0.6	0.04	-1.97	1.06	30.31	0.02
0.7	0.05	-1.82	1.36	31.79	0.03
0.8	0.05	-1.67	1.65	33.26	0.05
0.9	0.05	-1.53	1.95	34.73	0.06
1.0	0.08	-1.38	2.24	36.20	0.08
1.1	0.08	-1.23	2.54	37.68	0.11
1.2	0.15	-1.08	2.83	39.15	0.14
1.3	0.15	-0.94	3.12	40.62	0.17
1.4	0.19	-0.79	3.42	42.10	0.21
1.5	0.28	-0.64	3.71	43.57	0.26
1.6	0.28	-0.50	4.01	45.04	0.31
1.7	0.35	-0.35	4.30	46.51	0.36
1.8	0.35	-0.20	4.60	47.99	0.42
1.9	0.46	-0.05	4.89	49.46	0.48
2.0	0.58	0.09	5.19	50.93	0.54
2.1	0.58	0.24	5.48	52.40	0.60
2.2	0.68	0.39	5.78	53.88	0.65
2.3	0.68	0.54	6.07	55.35	0.70
2.4	0.76	0.68	6.36	56.82	0.75
2.5	0.82	0.83	6.66	58.30	0.80
2.6	0.82	0.98	6.95	59.77	0.84
2.7	0.87	1.12	7.25	61.24	0.87
2.8	0.87	1.27	7.54	62.71	0.90
2.9	0.91	1.42	7.84	64.19	0.92
3.0	1.00	1.57	8.13	65.66	0.94

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.09	1.00	19.08	0.00
0.1	0.00	-2.93	1.00	20.68	0.00
0.2	0.01	-2.77	1.00	22.28	0.00
0.3	0.03	-2.61	1.00	23.88	0.00
0.4	0.03	-2.45	1.00	25.48	0.01
0.5	0.03	-2.29	1.00	27.08	0.01
0.6	0.05	-2.13	1.00	28.68	0.02
0.7	0.05	-1.97	1.06	30.28	0.02
0.8	0.05	-1.81	1.37	31.87	0.03
0.9	0.05	-1.65	1.69	33.47	0.05
1.0	0.05	-1.49	2.01	35.07	0.07
1.1	0.05	-1.33	2.33	36.67	0.09
1.2	0.09	-1.17	2.65	38.27	0.12
1.3	0.15	-1.01	2.97	39.87	0.16
1.4	0.15	-0.85	3.29	41.47	0.20
1.5	0.24	-0.69	3.61	43.07	0.24
1.6	0.29	-0.53	3.93	44.67	0.30
1.7	0.29	-0.37	4.25	46.27	0.35
1.8	0.41	-0.21	4.57	47.87	0.42
1.9	0.47	-0.05	4.89	49.47	0.48
2.0	0.63	0.11	5.21	51.07	0.54
2.1	0.63	0.27	5.53	52.67	0.61
2.2	0.70	0.43	5.85	54.27	0.67
2.3	0.76	0.59	6.17	55.87	0.72
2.4	0.76	0.75	6.49	57.47	0.77
2.5	0.78	0.91	6.81	59.07	0.82
2.6	0.85	1.07	7.13	60.67	0.86
2.7	0.85	1.23	7.45	62.27	0.89
2.8	0.90	1.39	7.77	63.87	0.92
2.9	0.94	1.55	8.09	65.47	0.94
3.0	1.00	1.71	8.41	67.07	0.96

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.42	1.00	15.83	0.00
0.1	0.00	-3.24	1.00	17.64	0.00
0.2	0.00	-3.05	1.00	19.45	0.00
0.3	0.01	-2.87	1.00	21.27	0.00
0.4	0.01	-2.69	1.00	23.08	0.00
0.5	0.04	-2.51	1.00	24.89	0.01
0.6	0.04	-2.33	1.00	26.70	0.01
0.7	0.04	-2.15	1.00	28.52	0.02
0.8	0.05	-1.97	1.07	30.33	0.02
0.9	0.05	-1.79	1.43	32.14	0.04
1.0	0.05	-1.60	1.79	33.95	0.05
1.1	0.08	-1.42	2.15	35.77	0.08
1.2	0.08	-1.24	2.52	37.58	0.11
1.3	0.09	-1.06	2.88	39.39	0.14
1.4	0.13	-0.88	3.24	41.21	0.19
1.5	0.24	-0.70	3.60	43.02	0.24
1.6	0.30	-0.52	3.97	44.83	0.30
1.7	0.35	-0.34	4.33	46.64	0.37
1.8	0.44	-0.15	4.69	48.46	0.44
1.9	0.49	0.03	5.05	50.27	0.51
2.0	0.63	0.21	5.42	52.08	0.58
2.1	0.68	0.39	5.78	53.89	0.65
2.2	0.71	0.57	6.14	55.71	0.72
2.3	0.77	0.75	6.50	57.52	0.77
2.4	0.80	0.93	6.87	59.33	0.82
2.5	0.89	1.11	7.23	61.14	0.87
2.6	0.90	1.30	7.59	62.96	0.90
2.7	0.90	1.48	7.95	64.77	0.93
2.8	1.00	1.66	8.32	66.58	0.95
2.9	1.00	1.84	8.68	68.40	0.97
3.0	1.00	2.02	9.00	70.21	0.98

Group: Once a year $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.76	1.00	12.37	0.00
0.1	0.00	-3.54	1.00	14.57	0.00
0.2	0.00	-3.32	1.00	16.77	0.00
0.3	0.00	-3.10	1.00	18.96	0.00
0.4	0.00	-2.88	1.00	21.16	0.00
0.5	0.00	-2.66	1.00	23.36	0.00
0.6	0.02	-2.44	1.00	25.56	0.01
0.7	0.02	-2.22	1.00	27.76	0.01
0.8	0.02	-2.00	1.00	29.96	0.02
0.9	0.02	-1.78	1.43	32.15	0.04
1.0	0.07	-1.56	1.87	34.35	0.06
1.1	0.07	-1.34	2.31	36.55	0.09
1.2	0.10	-1.13	2.75	38.75	0.13
1.3	0.14	-0.91	3.19	40.95	0.18
1.4	0.21	-0.69	3.63	43.15	0.25
1.5	0.38	-0.47	4.07	45.34	0.32
1.6	0.45	-0.25	4.51	47.54	0.40
1.7	0.52	-0.03	4.95	49.74	0.49
1.8	0.66	0.19	5.39	51.94	0.58
1.9	0.67	0.41	5.83	54.14	0.66
2.0	0.79	0.63	6.27	56.33	0.74
2.1	0.83	0.85	6.71	58.53	0.80
2.2	0.83	1.07	7.15	60.73	0.86
2.3	0.90	1.29	7.59	62.93	0.90
2.4	0.91	1.51	8.03	65.13	0.93
2.5	0.95	1.73	8.47	67.33	0.96
2.6	0.97	1.95	8.90	69.52	0.97
2.7	0.98	2.17	9.00	71.72	0.99
2.8	0.98	2.39	9.00	73.92	0.99
2.9	0.98	2.61	9.00	76.12	1.00
3.0	1.00	2.83	9.00	78.32	1.00

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.04	1.00	19.58	0.00
0.1	0.00	-2.86	1.00	21.39	0.00
0.2	0.02	-2.68	1.00	23.20	0.00
0.3	0.02	-2.50	1.00	25.01	0.01
0.4	0.02	-2.32	1.00	26.82	0.01
0.5	0.02	-2.14	1.00	28.63	0.02
0.6	0.02	-1.96	1.09	30.44	0.03
0.7	0.03	-1.78	1.45	32.25	0.04
0.8	0.03	-1.59	1.81	34.06	0.06
0.9	0.05	-1.41	2.17	35.87	0.08
1.0	0.14	-1.23	2.54	37.68	0.11
1.1	0.14	-1.05	2.90	39.49	0.15
1.2	0.21	-0.87	3.26	41.29	0.19
1.3	0.21	-0.69	3.62	43.10	0.25
1.4	0.33	-0.51	3.98	44.91	0.31
1.5	0.43	-0.33	4.34	46.72	0.37
1.6	0.43	-0.15	4.71	48.53	0.44
1.7	0.57	0.03	5.07	50.34	0.51
1.8	0.57	0.22	5.43	52.15	0.59
1.9	0.67	0.40	5.79	53.96	0.65
2.0	0.79	0.58	6.15	55.77	0.72
2.1	0.79	0.76	6.52	57.58	0.78
2.2	0.86	0.94	6.88	59.39	0.83
2.3	0.86	1.12	7.24	61.20	0.87
2.4	0.88	1.30	7.60	63.01	0.90
2.5	0.95	1.48	7.96	64.82	0.93
2.6	0.95	1.66	8.33	66.63	0.95
2.7	0.97	1.84	8.69	68.44	0.97
2.8	0.97	2.02	9.00	70.25	0.98
2.9	0.98	2.21	9.00	72.06	0.99
3.0	1.00	2.39	9.00	73.87	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.50	1.00	14.98	0.00
0.1	0.00	-3.30	1.00	17.00	0.00
0.2	0.00	-3.10	1.00	19.02	0.00
0.3	0.00	-2.90	1.00	21.04	0.00
0.4	0.00	-2.69	1.00	23.06	0.00
0.5	0.00	-2.49	1.00	25.08	0.01
0.6	0.00	-2.29	1.00	27.10	0.01
0.7	0.00	-2.09	1.00	29.12	0.02
0.8	0.02	-1.89	1.23	31.14	0.03
0.9	0.03	-1.68	1.63	33.16	0.05
1.0	0.09	-1.48	2.04	35.18	0.07
1.1	0.09	-1.28	2.44	37.20	0.10
1.2	0.10	-1.08	2.84	39.22	0.14
1.3	0.19	-0.88	3.25	41.24	0.19
1.4	0.19	-0.67	3.65	43.26	0.25
1.5	0.31	-0.47	4.05	45.27	0.32
1.6	0.53	-0.27	4.46	47.29	0.39
1.7	0.53	-0.07	4.86	49.31	0.47
1.8	0.57	0.13	5.27	51.33	0.55
1.9	0.69	0.34	5.67	53.35	0.63
2.0	0.79	0.54	6.07	55.37	0.70
2.1	0.79	0.74	6.48	57.39	0.77
2.2	0.86	0.94	6.88	59.41	0.83
2.3	0.91	1.14	7.29	61.43	0.87
2.4	0.91	1.34	7.69	63.45	0.91
2.5	0.91	1.55	8.09	65.47	0.94
2.6	0.93	1.75	8.50	67.49	0.96
2.7	0.93	1.95	8.90	69.51	0.97
2.8	0.93	2.15	9.00	71.53	0.98
2.9	0.98	2.35	9.00	73.55	0.99
3.0	1.00	2.56	9.00	75.57	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.76	1.00	12.37	0.00
0.1	0.00	-3.54	1.00	14.57	0.00
0.2	0.00	-3.32	1.00	16.77	0.00
0.3	0.00	-3.10	1.00	18.96	0.00
0.4	0.00	-2.88	1.00	21.16	0.00
0.5	0.00	-2.66	1.00	23.36	0.00
0.6	0.02	-2.44	1.00	25.56	0.01
0.7	0.02	-2.22	1.00	27.76	0.01
0.8	0.02	-2.00	1.00	29.96	0.02
0.9	0.02	-1.78	1.43	32.15	0.04
1.0	0.07	-1.56	1.87	34.35	0.06
1.1	0.07	-1.34	2.31	36.55	0.09
1.2	0.10	-1.13	2.75	38.75	0.13
1.3	0.14	-0.91	3.19	40.95	0.18
1.4	0.21	-0.69	3.63	43.15	0.25
1.5	0.38	-0.47	4.07	45.34	0.32
1.6	0.45	-0.25	4.51	47.54	0.40
1.7	0.52	-0.03	4.95	49.74	0.49
1.8	0.66	0.19	5.39	51.94	0.58
1.9	0.67	0.41	5.83	54.14	0.66
2.0	0.79	0.63	6.27	56.33	0.74
2.1	0.83	0.85	6.71	58.53	0.80
2.2	0.83	1.07	7.15	60.73	0.86
2.3	0.90	1.29	7.59	62.93	0.90
2.4	0.91	1.51	8.03	65.13	0.93
2.5	0.95	1.73	8.47	67.33	0.96
2.6	0.97	1.95	8.90	69.52	0.97
2.7	0.98	2.17	9.00	71.72	0.99
2.8	0.98	2.39	9.00	73.92	0.99
2.9	0.98	2.61	9.00	76.12	1.00
3.0	1.00	2.83	9.00	78.32	1.00

7.4 Split by Vipassana continuously

7.4.1 Stats

describe_fmi_stats(data = d_w_items,
                   var = Vip_regel)

Vip_regel=ja
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.71	0.57	0.64	(0.29, 3.00)	1.43, 2.14	-0.02	0.04	33
fmi13_mean	1.67	0.56	0.59	(0.43, 2.79)	1.36, 2.14	-0.21	0.02	33
fmi14_mean	1.67	0.56	0.59	(0.43, 2.79)	1.36, 2.14	-0.21	0.02	33
presence_mean	1.66	0.55	0.77	(0.00, 3.00)	1.33, 2.17	-0.37	-0.18	33

Vip_regel=nicht
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.73	0.58	0.58	(0.00, 3.00)	1.43, 2.00	-0.22	0.28	979
fmi13_mean	1.71	0.57	0.51	(0.21, 3.00)	1.36, 2.00	-0.14	0.16	979
fmi14_mean	1.71	0.57	0.51	(0.21, 3.00)	1.36, 2.00	-0.14	0.16	979
presence_mean	1.70	0.57	0.59	(0.00, 3.00)	1.33, 2.00	-0.22	0.19	979

plot_fmi_descriptives(data = d_w_items,
                      var = Vip_regel)

7.4.2 Norms

for (i in unique(d_w_items$Vip_regel)) { 
  cat("Group: ", i, "\n")
  d_w_items %>% 
    filter(Vip_regel == i) %>% 
    select(ends_with("_mean")) %>% 
    map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                       digits = 2)) %>% 
    print()
}

Group: nicht $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.14	0.00
0.1	0.00	-3.19	1.00	18.11	0.00
0.2	0.00	-2.99	1.00	20.09	0.00
0.3	0.01	-2.79	1.00	22.06	0.00
0.4	0.01	-2.60	1.00	24.04	0.00
0.5	0.01	-2.40	1.00	26.01	0.01
0.6	0.02	-2.20	1.00	27.99	0.01
0.7	0.03	-2.00	1.00	29.96	0.02
0.8	0.04	-1.81	1.39	31.93	0.04
0.9	0.05	-1.61	1.78	33.91	0.05
1.0	0.09	-1.41	2.18	35.88	0.08
1.1	0.12	-1.21	2.57	37.86	0.11
1.2	0.15	-1.02	2.97	39.83	0.15
1.3	0.21	-0.82	3.36	41.81	0.21
1.4	0.25	-0.62	3.76	43.78	0.27
1.5	0.34	-0.42	4.15	45.76	0.34
1.6	0.39	-0.23	4.55	47.73	0.41
1.7	0.45	-0.03	4.94	49.70	0.49
1.8	0.58	0.17	5.34	51.68	0.57
1.9	0.63	0.37	5.73	53.65	0.64
2.0	0.76	0.56	6.13	55.63	0.71
2.1	0.80	0.76	6.52	57.60	0.78
2.2	0.83	0.96	6.92	59.58	0.83
2.3	0.89	1.16	7.31	61.55	0.88
2.4	0.91	1.35	7.71	63.53	0.91
2.5	0.95	1.55	8.10	65.50	0.94
2.6	0.96	1.75	8.50	67.48	0.96
2.7	0.97	1.94	8.89	69.45	0.97
2.8	0.99	2.14	9.00	71.42	0.98
2.9	0.99	2.34	9.00	73.40	0.99
3.0	1.00	2.54	9.00	75.37	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.90	1.00	21.04	0.00
0.1	0.01	-2.73	1.00	22.75	0.00
0.2	0.01	-2.55	1.00	24.45	0.01
0.3	0.01	-2.38	1.00	26.16	0.01
0.4	0.02	-2.21	1.00	27.86	0.01
0.5	0.04	-2.04	1.00	29.56	0.02
0.6	0.04	-1.87	1.25	31.27	0.03
0.7	0.06	-1.70	1.59	32.97	0.04
0.8	0.06	-1.53	1.94	34.68	0.06
0.9	0.09	-1.36	2.28	36.38	0.09
1.0	0.14	-1.19	2.62	38.09	0.12
1.1	0.14	-1.02	2.96	39.79	0.15
1.2	0.21	-0.85	3.30	41.50	0.20
1.3	0.21	-0.68	3.64	43.20	0.25
1.4	0.29	-0.51	3.98	44.91	0.31
1.5	0.40	-0.34	4.32	46.61	0.37
1.6	0.40	-0.17	4.66	48.32	0.43
1.7	0.51	0.00	5.00	50.02	0.50
1.8	0.51	0.17	5.35	51.73	0.57
1.9	0.64	0.34	5.69	53.43	0.63
2.0	0.77	0.51	6.03	55.14	0.70
2.1	0.77	0.68	6.37	56.84	0.75
2.2	0.84	0.85	6.71	58.55	0.80
2.3	0.84	1.03	7.05	60.25	0.85
2.4	0.89	1.20	7.39	61.96	0.88
2.5	0.94	1.37	7.73	63.66	0.91
2.6	0.94	1.54	8.07	65.37	0.94
2.7	0.96	1.71	8.41	67.07	0.96
2.8	0.96	1.88	8.76	68.78	0.97
2.9	0.98	2.05	9.00	70.48	0.98
3.0	1.00	2.22	9.00	72.19	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-3.00	1.00	19.96	0.00
0.1	0.01	-2.83	1.00	21.69	0.00
0.2	0.01	-2.66	1.00	23.42	0.00
0.3	0.02	-2.48	1.00	25.15	0.01
0.4	0.02	-2.31	1.00	26.88	0.01
0.5	0.03	-2.14	1.00	28.62	0.02
0.6	0.03	-1.97	1.07	30.35	0.02
0.7	0.03	-1.79	1.42	32.08	0.04
0.8	0.05	-1.62	1.76	33.81	0.05
0.9	0.08	-1.45	2.11	35.54	0.07
1.0	0.13	-1.27	2.46	37.28	0.10
1.1	0.13	-1.10	2.80	39.01	0.14
1.2	0.17	-0.93	3.15	40.74	0.18
1.3	0.24	-0.75	3.49	42.47	0.23
1.4	0.24	-0.58	3.84	44.20	0.28
1.5	0.33	-0.41	4.19	45.93	0.34
1.6	0.42	-0.23	4.53	47.67	0.41
1.7	0.42	-0.06	4.88	49.40	0.48
1.8	0.51	0.11	5.23	51.13	0.55
1.9	0.63	0.29	5.57	52.86	0.61
2.0	0.75	0.46	5.92	54.59	0.68
2.1	0.75	0.63	6.27	56.33	0.74
2.2	0.82	0.81	6.61	58.06	0.79
2.3	0.87	0.98	6.96	59.79	0.84
2.4	0.87	1.15	7.30	61.52	0.88
2.5	0.90	1.33	7.65	63.25	0.91
2.6	0.94	1.50	8.00	64.99	0.93
2.7	0.94	1.67	8.34	66.72	0.95
2.8	0.96	1.85	8.69	68.45	0.97
2.9	0.98	2.02	9.00	70.18	0.98
3.0	1.00	2.19	9.00	71.91	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.14	0.00
0.1	0.00	-3.19	1.00	18.11	0.00
0.2	0.00	-2.99	1.00	20.09	0.00
0.3	0.01	-2.79	1.00	22.06	0.00
0.4	0.01	-2.60	1.00	24.04	0.00
0.5	0.01	-2.40	1.00	26.01	0.01
0.6	0.02	-2.20	1.00	27.99	0.01
0.7	0.03	-2.00	1.00	29.96	0.02
0.8	0.04	-1.81	1.39	31.93	0.04
0.9	0.05	-1.61	1.78	33.91	0.05
1.0	0.09	-1.41	2.18	35.88	0.08
1.1	0.12	-1.21	2.57	37.86	0.11
1.2	0.15	-1.02	2.97	39.83	0.15
1.3	0.21	-0.82	3.36	41.81	0.21
1.4	0.25	-0.62	3.76	43.78	0.27
1.5	0.34	-0.42	4.15	45.76	0.34
1.6	0.39	-0.23	4.55	47.73	0.41
1.7	0.45	-0.03	4.94	49.70	0.49
1.8	0.58	0.17	5.34	51.68	0.57
1.9	0.63	0.37	5.73	53.65	0.64
2.0	0.76	0.56	6.13	55.63	0.71
2.1	0.80	0.76	6.52	57.60	0.78
2.2	0.83	0.96	6.92	59.58	0.83
2.3	0.89	1.16	7.31	61.55	0.88
2.4	0.91	1.35	7.71	63.53	0.91
2.5	0.95	1.55	8.10	65.50	0.94
2.6	0.96	1.75	8.50	67.48	0.96
2.7	0.97	1.94	8.89	69.45	0.97
2.8	0.99	2.14	9.00	71.42	0.98
2.9	0.99	2.34	9.00	73.40	0.99
3.0	1.00	2.54	9.00	75.37	0.99

Group: ja $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-2.82	1.00	21.78	0.00
0.1	0.00	-2.65	1.00	23.47	0.00
0.2	0.00	-2.48	1.00	25.16	0.01
0.3	0.00	-2.31	1.00	26.85	0.01
0.4	0.00	-2.15	1.00	28.55	0.02
0.5	0.06	-1.98	1.05	30.24	0.02
0.6	0.09	-1.81	1.39	31.93	0.04
0.7	0.09	-1.64	1.72	33.62	0.05
0.8	0.09	-1.47	2.06	35.31	0.07
0.9	0.09	-1.30	2.40	37.00	0.10
1.0	0.12	-1.13	2.74	38.69	0.13
1.1	0.12	-0.96	3.08	40.38	0.17
1.2	0.12	-0.79	3.41	42.07	0.21
1.3	0.21	-0.62	3.75	43.76	0.27
1.4	0.27	-0.45	4.09	45.45	0.32
1.5	0.39	-0.29	4.43	47.15	0.39
1.6	0.52	-0.12	4.77	48.84	0.45
1.7	0.52	0.05	5.11	50.53	0.52
1.8	0.70	0.22	5.44	52.22	0.59
1.9	0.73	0.39	5.78	53.91	0.65
2.0	0.73	0.56	6.12	55.60	0.71
2.1	0.73	0.73	6.46	57.29	0.77
2.2	0.79	0.90	6.80	58.98	0.82
2.3	0.85	1.07	7.13	60.67	0.86
2.4	0.88	1.24	7.47	62.36	0.89
2.5	0.94	1.41	7.81	64.05	0.92
2.6	0.94	1.57	8.15	65.75	0.94
2.7	0.94	1.74	8.49	67.44	0.96
2.8	1.00	1.91	8.83	69.13	0.97
2.9	1.00	2.08	9.00	70.82	0.98
3.0	1.00	2.25	9.00	72.51	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.03	-2.16	1.00	28.37	0.02
0.1	0.03	-2.03	1.00	29.68	0.02
0.2	0.09	-1.90	1.20	30.98	0.03
0.3	0.09	-1.77	1.46	32.29	0.04
0.4	0.09	-1.64	1.72	33.59	0.05
0.5	0.09	-1.51	1.98	34.90	0.07
0.6	0.09	-1.38	2.24	36.21	0.08
0.7	0.12	-1.25	2.50	37.51	0.11
0.8	0.12	-1.12	2.76	38.82	0.13
0.9	0.15	-0.99	3.02	40.12	0.16
1.0	0.21	-0.86	3.29	41.43	0.20
1.1	0.21	-0.73	3.55	42.73	0.23
1.2	0.24	-0.60	3.81	44.04	0.28
1.3	0.24	-0.47	4.07	45.34	0.32
1.4	0.30	-0.33	4.33	46.65	0.37
1.5	0.45	-0.20	4.59	47.96	0.42
1.6	0.45	-0.07	4.85	49.26	0.47
1.7	0.58	0.06	5.11	50.57	0.52
1.8	0.58	0.19	5.37	51.87	0.57
1.9	0.67	0.32	5.64	53.18	0.62
2.0	0.67	0.45	5.90	54.48	0.67
2.1	0.67	0.58	6.16	55.79	0.72
2.2	0.76	0.71	6.42	57.09	0.76
2.3	0.76	0.84	6.68	58.40	0.80
2.4	0.82	0.97	6.94	59.71	0.83
2.5	0.91	1.10	7.20	61.01	0.86
2.6	0.91	1.23	7.46	62.32	0.89
2.7	0.91	1.36	7.72	63.62	0.91
2.8	0.91	1.49	7.99	64.93	0.93
2.9	0.97	1.62	8.25	66.23	0.95
3.0	1.00	1.75	8.51	67.54	0.96

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-2.69	1.00	23.09	0.00
0.1	0.00	-2.53	1.00	24.66	0.01
0.2	0.00	-2.38	1.00	26.23	0.01
0.3	0.03	-2.22	1.00	27.81	0.01
0.4	0.03	-2.06	1.00	29.38	0.02
0.5	0.03	-1.90	1.19	30.96	0.03
0.6	0.06	-1.75	1.51	32.53	0.04
0.7	0.06	-1.59	1.82	34.10	0.06
0.8	0.09	-1.43	2.14	35.68	0.08
0.9	0.12	-1.27	2.45	37.25	0.10
1.0	0.12	-1.12	2.77	38.83	0.13
1.1	0.12	-0.96	3.08	40.40	0.17
1.2	0.18	-0.80	3.39	41.97	0.21
1.3	0.24	-0.65	3.71	43.55	0.26
1.4	0.24	-0.49	4.02	45.12	0.31
1.5	0.33	-0.33	4.34	46.70	0.37
1.6	0.45	-0.17	4.65	48.27	0.43
1.7	0.45	-0.02	4.97	49.84	0.49
1.8	0.64	0.14	5.28	51.42	0.56
1.9	0.67	0.30	5.60	52.99	0.62
2.0	0.73	0.46	5.91	54.57	0.68
2.1	0.73	0.61	6.23	56.14	0.73
2.2	0.82	0.77	6.54	57.71	0.78
2.3	0.85	0.93	6.86	59.29	0.82
2.4	0.85	1.09	7.17	60.86	0.86
2.5	0.85	1.24	7.49	62.43	0.89
2.6	0.91	1.40	7.80	64.01	0.92
2.7	0.91	1.56	8.12	65.58	0.94
2.8	0.94	1.72	8.43	67.16	0.96
2.9	0.97	1.87	8.75	68.73	0.97
3.0	1.00	2.03	9.00	70.30	0.98

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-2.82	1.00	21.78	0.00
0.1	0.00	-2.65	1.00	23.47	0.00
0.2	0.00	-2.48	1.00	25.16	0.01
0.3	0.00	-2.31	1.00	26.85	0.01
0.4	0.00	-2.15	1.00	28.55	0.02
0.5	0.06	-1.98	1.05	30.24	0.02
0.6	0.09	-1.81	1.39	31.93	0.04
0.7	0.09	-1.64	1.72	33.62	0.05
0.8	0.09	-1.47	2.06	35.31	0.07
0.9	0.09	-1.30	2.40	37.00	0.10
1.0	0.12	-1.13	2.74	38.69	0.13
1.1	0.12	-0.96	3.08	40.38	0.17
1.2	0.12	-0.79	3.41	42.07	0.21
1.3	0.21	-0.62	3.75	43.76	0.27
1.4	0.27	-0.45	4.09	45.45	0.32
1.5	0.39	-0.29	4.43	47.15	0.39
1.6	0.52	-0.12	4.77	48.84	0.45
1.7	0.52	0.05	5.11	50.53	0.52
1.8	0.70	0.22	5.44	52.22	0.59
1.9	0.73	0.39	5.78	53.91	0.65
2.0	0.73	0.56	6.12	55.60	0.71
2.1	0.73	0.73	6.46	57.29	0.77
2.2	0.79	0.90	6.80	58.98	0.82
2.3	0.85	1.07	7.13	60.67	0.86
2.4	0.88	1.24	7.47	62.36	0.89
2.5	0.94	1.41	7.81	64.05	0.92
2.6	0.94	1.57	8.15	65.75	0.94
2.7	0.94	1.74	8.49	67.44	0.96
2.8	1.00	1.91	8.83	69.13	0.97
2.9	1.00	2.08	9.00	70.82	0.98
3.0	1.00	2.25	9.00	72.51	0.99

7.5 Split by Age

7.5.1 Stats

Median age in sample?

d_w_items$Alter %>% median()

## [1] 49

d_w_items <-
  d_w_items %>%
  mutate(age_below_md = if_else(Alter < median(Alter), "young", "old"))

describe_fmi_stats(data = d_w_items,
                   var = age_below_md)

age_below_md=old
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.76	0.59	0.59	(0.00, 3.00)	1.43, 2.14	-0.38	0.41	526
fmi13_mean	1.74	0.58	0.51	(0.21, 3.00)	1.43, 2.07	-0.29	0.25	526
fmi14_mean	1.74	0.58	0.51	(0.21, 3.00)	1.43, 2.07	-0.29	0.25	526
presence_mean	1.71	0.57	0.58	(0.00, 3.00)	1.33, 2.00	-0.38	0.39	526

age_below_md=young
Variable	Mean	Mean_01	SD	Range	Quartiles	Skewness	Kurtosis	n
acceptance13_mean	1.70	0.57	0.56	(0.00, 3.00)	1.29, 2.00	-0.03	0.17	486
fmi13_mean	1.68	0.56	0.50	(0.21, 3.00)	1.36, 2.00	0.01	0.14	486
fmi14_mean	1.68	0.56	0.50	(0.21, 3.00)	1.36, 2.00	0.01	0.14	486
presence_mean	1.68	0.56	0.60	(0.00, 3.00)	1.33, 2.00	-0.09	0.05	486

plot_fmi_descriptives(data = d_w_items,
                      var = age_below_md)

7.5.2 Norms

for (i in unique(d_w_items$age_below_md)) { 
  cat("Group: ", i, "\n")
  d_w_items %>% 
    filter(age_below_md == i) %>% 
    select(ends_with("_mean")) %>% 
    map(~ knitr::kable(compute_all_norms(., min_score = 0, max_score = 3, by = .1), 
                       digits = 2)) %>% 
    print()
}

Group: young $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.34	1.00	16.56	0.00
0.1	0.00	-3.14	1.00	18.55	0.00
0.2	0.00	-2.95	1.00	20.54	0.00
0.3	0.01	-2.75	1.00	22.53	0.00
0.4	0.01	-2.55	1.00	24.52	0.01
0.5	0.01	-2.35	1.00	26.51	0.01
0.6	0.02	-2.15	1.00	28.50	0.02
0.7	0.02	-1.95	1.10	30.49	0.03
0.8	0.04	-1.75	1.49	32.47	0.04
0.9	0.06	-1.55	1.89	34.46	0.06
1.0	0.09	-1.35	2.29	36.45	0.09
1.1	0.12	-1.16	2.69	38.44	0.12
1.2	0.16	-0.96	3.09	40.43	0.17
1.3	0.22	-0.76	3.48	42.42	0.22
1.4	0.27	-0.56	3.88	44.41	0.29
1.5	0.39	-0.36	4.28	46.40	0.36
1.6	0.45	-0.16	4.68	48.38	0.44
1.7	0.50	0.04	5.07	50.37	0.51
1.8	0.62	0.24	5.47	52.36	0.59
1.9	0.66	0.44	5.87	54.35	0.67
2.0	0.78	0.63	6.27	56.34	0.74
2.1	0.83	0.83	6.67	58.33	0.80
2.2	0.86	1.03	7.06	60.32	0.85
2.3	0.90	1.23	7.46	62.31	0.89
2.4	0.91	1.43	7.86	64.29	0.92
2.5	0.95	1.63	8.26	66.28	0.95
2.6	0.96	1.83	8.65	68.27	0.97
2.7	0.96	2.03	9.00	70.26	0.98
2.8	0.99	2.22	9.00	72.25	0.99
2.9	0.99	2.42	9.00	74.24	0.99
3.0	1.00	2.62	9.00	76.23	1.00

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.78	1.00	22.23	0.00
0.1	0.01	-2.61	1.00	23.89	0.00
0.2	0.02	-2.45	1.00	25.54	0.01
0.3	0.02	-2.28	1.00	27.20	0.01
0.4	0.02	-2.11	1.00	28.85	0.02
0.5	0.03	-1.95	1.10	30.51	0.03
0.6	0.03	-1.78	1.43	32.16	0.04
0.7	0.07	-1.62	1.76	33.82	0.05
0.8	0.07	-1.45	2.09	35.47	0.07
0.9	0.10	-1.29	2.42	37.12	0.10
1.0	0.15	-1.12	2.76	38.78	0.13
1.1	0.15	-0.96	3.09	40.43	0.17
1.2	0.23	-0.79	3.42	42.09	0.21
1.3	0.23	-0.63	3.75	43.74	0.27
1.4	0.31	-0.46	4.08	45.40	0.32
1.5	0.43	-0.30	4.41	47.05	0.38
1.6	0.43	-0.13	4.74	48.70	0.45
1.7	0.56	0.04	5.07	50.36	0.51
1.8	0.56	0.20	5.40	52.01	0.58
1.9	0.66	0.37	5.73	53.67	0.64
2.0	0.77	0.53	6.06	55.32	0.70
2.1	0.77	0.70	6.40	56.98	0.76
2.2	0.84	0.86	6.73	58.63	0.81
2.3	0.84	1.03	7.06	60.28	0.85
2.4	0.88	1.19	7.39	61.94	0.88
2.5	0.92	1.36	7.72	63.59	0.91
2.6	0.92	1.52	8.05	65.25	0.94
2.7	0.95	1.69	8.38	66.90	0.95
2.8	0.95	1.86	8.71	68.56	0.97
2.9	0.97	2.02	9.00	70.21	0.98
3.0	1.00	2.19	9.00	71.86	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.03	1.00	19.67	0.00
0.1	0.00	-2.85	1.00	21.45	0.00
0.2	0.01	-2.68	1.00	23.23	0.00
0.3	0.01	-2.50	1.00	25.02	0.01
0.4	0.01	-2.32	1.00	26.80	0.01
0.5	0.02	-2.14	1.00	28.58	0.02
0.6	0.03	-1.96	1.07	30.36	0.02
0.7	0.03	-1.79	1.43	32.14	0.04
0.8	0.04	-1.61	1.78	33.92	0.05
0.9	0.08	-1.43	2.14	35.70	0.08
1.0	0.13	-1.25	2.50	37.49	0.11
1.1	0.13	-1.07	2.85	39.27	0.14
1.2	0.18	-0.90	3.21	41.05	0.19
1.3	0.26	-0.72	3.57	42.83	0.24
1.4	0.26	-0.54	3.92	44.61	0.29
1.5	0.35	-0.36	4.28	46.39	0.36
1.6	0.46	-0.18	4.63	48.17	0.43
1.7	0.46	0.00	4.99	49.95	0.50
1.8	0.55	0.17	5.35	51.74	0.57
1.9	0.66	0.35	5.70	53.52	0.64
2.0	0.78	0.53	6.06	55.30	0.70
2.1	0.78	0.71	6.42	57.08	0.76
2.2	0.84	0.89	6.77	58.86	0.81
2.3	0.89	1.06	7.13	60.64	0.86
2.4	0.89	1.24	7.48	62.42	0.89
2.5	0.91	1.42	7.84	64.21	0.92
2.6	0.94	1.60	8.20	65.99	0.95
2.7	0.94	1.78	8.55	67.77	0.96
2.8	0.96	1.96	8.91	69.55	0.97
2.9	0.98	2.13	9.00	71.33	0.98
3.0	1.00	2.31	9.00	73.11	0.99

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.34	1.00	16.56	0.00
0.1	0.00	-3.14	1.00	18.55	0.00
0.2	0.00	-2.95	1.00	20.54	0.00
0.3	0.01	-2.75	1.00	22.53	0.00
0.4	0.01	-2.55	1.00	24.52	0.01
0.5	0.01	-2.35	1.00	26.51	0.01
0.6	0.02	-2.15	1.00	28.50	0.02
0.7	0.02	-1.95	1.10	30.49	0.03
0.8	0.04	-1.75	1.49	32.47	0.04
0.9	0.06	-1.55	1.89	34.46	0.06
1.0	0.09	-1.35	2.29	36.45	0.09
1.1	0.12	-1.16	2.69	38.44	0.12
1.2	0.16	-0.96	3.09	40.43	0.17
1.3	0.22	-0.76	3.48	42.42	0.22
1.4	0.27	-0.56	3.88	44.41	0.29
1.5	0.39	-0.36	4.28	46.40	0.36
1.6	0.45	-0.16	4.68	48.38	0.44
1.7	0.50	0.04	5.07	50.37	0.51
1.8	0.62	0.24	5.47	52.36	0.59
1.9	0.66	0.44	5.87	54.35	0.67
2.0	0.78	0.63	6.27	56.34	0.74
2.1	0.83	0.83	6.67	58.33	0.80
2.2	0.86	1.03	7.06	60.32	0.85
2.3	0.90	1.23	7.46	62.31	0.89
2.4	0.91	1.43	7.86	64.29	0.92
2.5	0.95	1.63	8.26	66.28	0.95
2.6	0.96	1.83	8.65	68.27	0.97
2.7	0.96	2.03	9.00	70.26	0.98
2.8	0.99	2.22	9.00	72.25	0.99
2.9	0.99	2.42	9.00	74.24	0.99
3.0	1.00	2.62	9.00	76.23	1.00

Group: old $fmi13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.06	0.00
0.1	0.00	-3.20	1.00	18.01	0.00
0.2	0.00	-3.00	1.00	19.96	0.00
0.3	0.01	-2.81	1.00	21.90	0.00
0.4	0.01	-2.61	1.00	23.85	0.00
0.5	0.02	-2.42	1.00	25.80	0.01
0.6	0.03	-2.23	1.00	27.74	0.01
0.7	0.03	-2.03	1.00	29.69	0.02
0.8	0.05	-1.84	1.33	31.64	0.03
0.9	0.05	-1.64	1.72	33.58	0.05
1.0	0.09	-1.45	2.11	35.53	0.07
1.1	0.12	-1.25	2.50	37.48	0.11
1.2	0.14	-1.06	2.88	39.42	0.15
1.3	0.20	-0.86	3.27	41.37	0.19
1.4	0.23	-0.67	3.66	43.32	0.25
1.5	0.29	-0.47	4.05	45.27	0.32
1.6	0.34	-0.28	4.44	47.21	0.39
1.7	0.41	-0.08	4.83	49.16	0.47
1.8	0.54	0.11	5.22	51.11	0.54
1.9	0.61	0.31	5.61	53.05	0.62
2.0	0.74	0.50	6.00	55.00	0.69
2.1	0.77	0.69	6.39	56.95	0.76
2.2	0.81	0.89	6.78	58.89	0.81
2.3	0.89	1.08	7.17	60.84	0.86
2.4	0.90	1.28	7.56	62.79	0.90
2.5	0.94	1.47	7.95	64.73	0.93
2.6	0.96	1.67	8.34	66.68	0.95
2.7	0.97	1.86	8.73	68.63	0.97
2.8	0.99	2.06	9.00	70.57	0.98
2.9	0.99	2.25	9.00	72.52	0.99
3.0	1.00	2.45	9.00	74.47	0.99

$presence_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.95	1.00	20.53	0.00
0.1	0.01	-2.78	1.00	22.25	0.00
0.2	0.01	-2.60	1.00	23.97	0.00
0.3	0.01	-2.43	1.00	25.69	0.01
0.4	0.03	-2.26	1.00	27.41	0.01
0.5	0.05	-2.09	1.00	29.12	0.02
0.6	0.05	-1.92	1.17	30.84	0.03
0.7	0.06	-1.74	1.51	32.56	0.04
0.8	0.06	-1.57	1.86	34.28	0.06
0.9	0.09	-1.40	2.20	36.00	0.08
1.0	0.14	-1.23	2.54	37.72	0.11
1.1	0.14	-1.06	2.89	39.43	0.15
1.2	0.19	-0.88	3.23	41.15	0.19
1.3	0.19	-0.71	3.57	42.87	0.24
1.4	0.28	-0.54	3.92	44.59	0.29
1.5	0.37	-0.37	4.26	46.31	0.36
1.6	0.37	-0.20	4.61	48.03	0.42
1.7	0.48	-0.03	4.95	49.75	0.49
1.8	0.48	0.15	5.29	51.46	0.56
1.9	0.61	0.32	5.64	53.18	0.62
2.0	0.77	0.49	5.98	54.90	0.69
2.1	0.77	0.66	6.32	56.62	0.75
2.2	0.84	0.83	6.67	58.34	0.80
2.3	0.84	1.01	7.01	60.06	0.84
2.4	0.90	1.18	7.35	61.77	0.88
2.5	0.94	1.35	7.70	63.49	0.91
2.6	0.94	1.52	8.04	65.21	0.94
2.7	0.96	1.69	8.39	66.93	0.95
2.8	0.96	1.86	8.73	68.65	0.97
2.9	0.98	2.04	9.00	70.37	0.98
3.0	1.00	2.21	9.00	72.09	0.99

$acceptance13_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.01	-2.97	1.00	20.32	0.00
0.1	0.01	-2.80	1.00	22.00	0.00
0.2	0.02	-2.63	1.00	23.69	0.00
0.3	0.02	-2.46	1.00	25.37	0.01
0.4	0.02	-2.29	1.00	27.05	0.01
0.5	0.03	-2.13	1.00	28.74	0.02
0.6	0.04	-1.96	1.08	30.42	0.03
0.7	0.04	-1.79	1.42	32.11	0.04
0.8	0.06	-1.62	1.76	33.79	0.05
0.9	0.08	-1.45	2.09	35.47	0.07
1.0	0.12	-1.28	2.43	37.16	0.10
1.1	0.12	-1.12	2.77	38.84	0.13
1.2	0.16	-0.95	3.10	40.52	0.17
1.3	0.23	-0.78	3.44	42.21	0.22
1.4	0.23	-0.61	3.78	43.89	0.27
1.5	0.30	-0.44	4.11	45.57	0.33
1.6	0.37	-0.27	4.45	47.26	0.39
1.7	0.37	-0.11	4.79	48.94	0.46
1.8	0.48	0.06	5.12	50.62	0.52
1.9	0.60	0.23	5.46	52.31	0.59
2.0	0.73	0.40	5.80	53.99	0.66
2.1	0.73	0.57	6.14	55.68	0.71
2.2	0.81	0.74	6.47	57.36	0.77
2.3	0.85	0.90	6.81	59.04	0.82
2.4	0.85	1.07	7.15	60.73	0.86
2.5	0.89	1.24	7.48	62.41	0.89
2.6	0.94	1.41	7.82	64.09	0.92
2.7	0.94	1.58	8.16	65.78	0.94
2.8	0.96	1.75	8.49	67.46	0.96
2.9	0.97	1.91	8.83	69.14	0.97
3.0	1.00	2.08	9.00	70.83	0.98

$fmi14_mean

score	perc_rank	z	stanine	T	perc_normal
0.0	0.00	-3.39	1.00	16.06	0.00
0.1	0.00	-3.20	1.00	18.01	0.00
0.2	0.00	-3.00	1.00	19.96	0.00
0.3	0.01	-2.81	1.00	21.90	0.00
0.4	0.01	-2.61	1.00	23.85	0.00
0.5	0.02	-2.42	1.00	25.80	0.01
0.6	0.03	-2.23	1.00	27.74	0.01
0.7	0.03	-2.03	1.00	29.69	0.02
0.8	0.05	-1.84	1.33	31.64	0.03
0.9	0.05	-1.64	1.72	33.58	0.05
1.0	0.09	-1.45	2.11	35.53	0.07
1.1	0.12	-1.25	2.50	37.48	0.11
1.2	0.14	-1.06	2.88	39.42	0.15
1.3	0.20	-0.86	3.27	41.37	0.19
1.4	0.23	-0.67	3.66	43.32	0.25
1.5	0.29	-0.47	4.05	45.27	0.32
1.6	0.34	-0.28	4.44	47.21	0.39
1.7	0.41	-0.08	4.83	49.16	0.47
1.8	0.54	0.11	5.22	51.11	0.54
1.9	0.61	0.31	5.61	53.05	0.62
2.0	0.74	0.50	6.00	55.00	0.69
2.1	0.77	0.69	6.39	56.95	0.76
2.2	0.81	0.89	6.78	58.89	0.81
2.3	0.89	1.08	7.17	60.84	0.86
2.4	0.90	1.28	7.56	62.79	0.90
2.5	0.94	1.47	7.95	64.73	0.93
2.6	0.96	1.67	8.34	66.68	0.95
2.7	0.97	1.86	8.73	68.63	0.97
2.8	0.99	2.06	9.00	70.57	0.98
2.9	0.99	2.25	9.00	72.52	0.99
3.0	1.00	2.45	9.00	74.47	0.99

8 Overview on descriptive statistics per subgroup

subgroup_stats <- list()

for (i in seq_along(subgroup_vars)){

subgroup_stats[[i]] <- 
  d_w_items %>% 
  select(ends_with("mean"),
         any_of(subgroup_vars)[i]) %>% 
  group_by(across(any_of(subgroup_vars[i]))) %>% 
    describe_distribution() %>% 
  select(Variable, Mean, SD, IQR, Min, Max, n, .group)

subgroup_stats[[i]][["subgroup_var"]] <- subgroup_vars[i]
}

subgroup_stats_df <- do.call(rbind, subgroup_stats)

subgroup_stats_df <-
  subgroup_stats_df %>% 
  mutate(group = str_remove(.group, "^.+=")) %>% 
  select(-.group)

display(subgroup_stats_df)

Variable	Mean	SD	IQR	Range	n	subgroup_var	group
fmi13_mean	1.71	0.51	0.71	(0.21, 3.00)	515	Geschlecht	female
presence_mean	1.72	0.58	0.67	(0.00, 3.00)	515	Geschlecht	female
acceptance13_mean	1.73	0.57	0.86	(0.00, 3.00)	515	Geschlecht	female
fmi14_mean	1.71	0.51	0.71	(0.21, 3.00)	515	Geschlecht	female
fmi13_mean	1.71	0.51	0.57	(0.21, 3.00)	495	Geschlecht	male
presence_mean	1.67	0.60	0.67	(0.00, 3.00)	495	Geschlecht	male
acceptance13_mean	1.74	0.59	0.57	(0.00, 3.00)	495	Geschlecht	male
fmi14_mean	1.71	0.51	0.57	(0.21, 3.00)	495	Geschlecht	male
fmi13_mean	1.50	0.20	0.29	(1.36, 1.64)	2	Geschlecht	other
presence_mean	1.33	0.00	0.00	(1.33, 1.33)	2	Geschlecht	other
acceptance13_mean	1.79	0.51	0.71	(1.43, 2.14)	2	Geschlecht	other
fmi14_mean	1.50	0.20	0.29	(1.36, 1.64)	2	Geschlecht	other
fmi13_mean	1.69	0.51	0.64	(0.21, 3.00)	792	Achts_regel	no
presence_mean	1.65	0.59	0.67	(0.00, 3.00)	792	Achts_regel	no
acceptance13_mean	1.72	0.59	0.71	(0.00, 3.00)	792	Achts_regel	no
fmi14_mean	1.69	0.51	0.64	(0.21, 3.00)	792	Achts_regel	no
fmi13_mean	1.81	0.49	0.57	(0.21, 3.00)	220	Achts_regel	yes
presence_mean	1.86	0.56	0.67	(0.00, 3.00)	220	Achts_regel	yes
acceptance13_mean	1.80	0.55	0.71	(0.00, 3.00)	220	Achts_regel	yes
fmi14_mean	1.81	0.49	0.57	(0.21, 3.00)	220	Achts_regel	yes
fmi13_mean	1.82	0.43	0.43	(0.71, 3.00)	116	Retreats	Multiple retreats per year
presence_mean	1.84	0.50	0.62	(0.33, 3.00)	116	Retreats	Multiple retreats per year
acceptance13_mean	1.81	0.48	0.54	(0.71, 3.00)	116	Retreats	Multiple retreats per year
fmi14_mean	1.82	0.43	0.43	(0.71, 3.00)	116	Retreats	Multiple retreats per year
fmi13_mean	1.68	0.52	0.64	(0.21, 3.00)	673	Retreats	Never
presence_mean	1.64	0.59	0.67	(0.00, 3.00)	673	Retreats	Never
acceptance13_mean	1.70	0.60	0.71	(0.00, 3.00)	673	Retreats	Never
fmi14_mean	1.68	0.52	0.64	(0.21, 3.00)	673	Retreats	Never
fmi13_mean	1.71	0.45	0.57	(0.57, 2.93)	58	Retreats	Once a year
presence_mean	1.68	0.55	0.67	(0.17, 3.00)	58	Retreats	Once a year
acceptance13_mean	1.73	0.50	0.57	(0.71, 3.00)	58	Retreats	Once a year
fmi14_mean	1.71	0.45	0.57	(0.57, 2.93)	58	Retreats	Once a year
fmi13_mean	1.71	0.46	0.71	(0.93, 2.93)	86	Retreats	Once every couple of years
presence_mean	1.71	0.59	0.83	(0.67, 3.00)	86	Retreats	Once every couple of years
acceptance13_mean	1.74	0.53	0.71	(0.29, 3.00)	86	Retreats	Once every couple of years
fmi14_mean	1.71	0.46	0.71	(0.93, 2.93)	86	Retreats	Once every couple of years
fmi13_mean	1.89	0.55	0.71	(0.29, 2.79)	79	Retreats	Rarely
presence_mean	1.94	0.68	0.83	(0.00, 3.00)	79	Retreats	Rarely
acceptance13_mean	1.93	0.63	0.71	(0.14, 3.00)	79	Retreats	Rarely
fmi14_mean	1.89	0.55	0.71	(0.29, 2.79)	79	Retreats	Rarely
fmi13_mean	1.67	0.59	0.79	(0.43, 2.79)	33	Vip_regel	ja
presence_mean	1.66	0.77	1.00	(0.00, 3.00)	33	Vip_regel	ja
acceptance13_mean	1.71	0.64	0.79	(0.29, 3.00)	33	Vip_regel	ja
fmi14_mean	1.67	0.59	0.79	(0.43, 2.79)	33	Vip_regel	ja
fmi13_mean	1.71	0.51	0.64	(0.21, 3.00)	979	Vip_regel	nicht
presence_mean	1.70	0.59	0.67	(0.00, 3.00)	979	Vip_regel	nicht
acceptance13_mean	1.73	0.58	0.57	(0.00, 3.00)	979	Vip_regel	nicht
fmi14_mean	1.71	0.51	0.64	(0.21, 3.00)	979	Vip_regel	nicht
fmi13_mean	1.74	0.51	0.64	(0.21, 3.00)	526	age_below_md	old
presence_mean	1.71	0.58	0.67	(0.00, 3.00)	526	age_below_md	old
acceptance13_mean	1.76	0.59	0.71	(0.00, 3.00)	526	age_below_md	old
fmi14_mean	1.74	0.51	0.64	(0.21, 3.00)	526	age_below_md	old
fmi13_mean	1.68	0.50	0.64	(0.21, 3.00)	486	age_below_md	young
presence_mean	1.68	0.60	0.67	(0.00, 3.00)	486	age_below_md	young
acceptance13_mean	1.70	0.56	0.71	(0.00, 3.00)	486	age_below_md	young
fmi14_mean	1.68	0.50	0.64	(0.21, 3.00)	486	age_below_md	young

subgroup_stats_long <- 
subgroup_stats_df %>% 
  select(Variable, Mean, SD, group, subgroup_var) %>% 
  mutate(Subscale = str_remove(Variable, "_mean")) %>% 
  pivot_longer(-c(Variable, group, Mean, Subscale, subgroup_var), 
               values_to = "SD")

display(subgroup_stats_long)

Variable	Mean	group	subgroup_var	Subscale	name	SD
fmi13_mean	1.71	female	Geschlecht	fmi13	SD	0.51
presence_mean	1.72	female	Geschlecht	presence	SD	0.58
acceptance13_mean	1.73	female	Geschlecht	acceptance13	SD	0.57
fmi14_mean	1.71	female	Geschlecht	fmi14	SD	0.51
fmi13_mean	1.71	male	Geschlecht	fmi13	SD	0.51
presence_mean	1.67	male	Geschlecht	presence	SD	0.60
acceptance13_mean	1.74	male	Geschlecht	acceptance13	SD	0.59
fmi14_mean	1.71	male	Geschlecht	fmi14	SD	0.51
fmi13_mean	1.50	other	Geschlecht	fmi13	SD	0.20
presence_mean	1.33	other	Geschlecht	presence	SD	0.00
acceptance13_mean	1.79	other	Geschlecht	acceptance13	SD	0.51
fmi14_mean	1.50	other	Geschlecht	fmi14	SD	0.20
fmi13_mean	1.69	no	Achts_regel	fmi13	SD	0.51
presence_mean	1.65	no	Achts_regel	presence	SD	0.59
acceptance13_mean	1.72	no	Achts_regel	acceptance13	SD	0.59
fmi14_mean	1.69	no	Achts_regel	fmi14	SD	0.51
fmi13_mean	1.81	yes	Achts_regel	fmi13	SD	0.49
presence_mean	1.86	yes	Achts_regel	presence	SD	0.56
acceptance13_mean	1.80	yes	Achts_regel	acceptance13	SD	0.55
fmi14_mean	1.81	yes	Achts_regel	fmi14	SD	0.49
fmi13_mean	1.82	Multiple retreats per year	Retreats	fmi13	SD	0.43
presence_mean	1.84	Multiple retreats per year	Retreats	presence	SD	0.50
acceptance13_mean	1.81	Multiple retreats per year	Retreats	acceptance13	SD	0.48
fmi14_mean	1.82	Multiple retreats per year	Retreats	fmi14	SD	0.43
fmi13_mean	1.68	Never	Retreats	fmi13	SD	0.52
presence_mean	1.64	Never	Retreats	presence	SD	0.59
acceptance13_mean	1.70	Never	Retreats	acceptance13	SD	0.60
fmi14_mean	1.68	Never	Retreats	fmi14	SD	0.52
fmi13_mean	1.71	Once a year	Retreats	fmi13	SD	0.45
presence_mean	1.68	Once a year	Retreats	presence	SD	0.55
acceptance13_mean	1.73	Once a year	Retreats	acceptance13	SD	0.50
fmi14_mean	1.71	Once a year	Retreats	fmi14	SD	0.45
fmi13_mean	1.71	Once every couple of years	Retreats	fmi13	SD	0.46
presence_mean	1.71	Once every couple of years	Retreats	presence	SD	0.59
acceptance13_mean	1.74	Once every couple of years	Retreats	acceptance13	SD	0.53
fmi14_mean	1.71	Once every couple of years	Retreats	fmi14	SD	0.46
fmi13_mean	1.89	Rarely	Retreats	fmi13	SD	0.55
presence_mean	1.94	Rarely	Retreats	presence	SD	0.68
acceptance13_mean	1.93	Rarely	Retreats	acceptance13	SD	0.63
fmi14_mean	1.89	Rarely	Retreats	fmi14	SD	0.55
fmi13_mean	1.67	ja	Vip_regel	fmi13	SD	0.59
presence_mean	1.66	ja	Vip_regel	presence	SD	0.77
acceptance13_mean	1.71	ja	Vip_regel	acceptance13	SD	0.64
fmi14_mean	1.67	ja	Vip_regel	fmi14	SD	0.59
fmi13_mean	1.71	nicht	Vip_regel	fmi13	SD	0.51
presence_mean	1.70	nicht	Vip_regel	presence	SD	0.59
acceptance13_mean	1.73	nicht	Vip_regel	acceptance13	SD	0.58
fmi14_mean	1.71	nicht	Vip_regel	fmi14	SD	0.51
fmi13_mean	1.74	old	age_below_md	fmi13	SD	0.51
presence_mean	1.71	old	age_below_md	presence	SD	0.58
acceptance13_mean	1.76	old	age_below_md	acceptance13	SD	0.59
fmi14_mean	1.74	old	age_below_md	fmi14	SD	0.51
fmi13_mean	1.68	young	age_below_md	fmi13	SD	0.50
presence_mean	1.68	young	age_below_md	presence	SD	0.60
acceptance13_mean	1.70	young	age_below_md	acceptance13	SD	0.56
fmi14_mean	1.68	young	age_below_md	fmi14	SD	0.50

# subgroup_stats_long %>% 
#   ggplot(aes(x = Variable, color = group)) +
#   geom_errorbar(aes(ymin = Mean-SD, ymax = Mean+SD), position = "dodge") +
#   geom_point2(aes(y = Mean), alpha = .7, size = 2) +
#   facet_wrap(subgroup_vars ~ Variable, scales = "free")

8.1 Regression models

8.1.1 m1

m1 <- lm(phq_sum ~ presence_mean + acceptance13_mean, data = d_w_items)
parameters(m1) %>% display()

performance(m1) %>% display
summary(m1)

Standardized data:

parameters(m1, standardize = "refit") %>% display

9 Session info

sessionInfo()

## R version 4.4.1 (2024-06-14)
## Platform: x86_64-apple-darwin20
## Running under: macOS 15.4.1
## 
## Matrix products: default
## BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
## LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0
## 
## locale:
## [1] de_DE.UTF-8/de_DE.UTF-8/de_DE.UTF-8/C/de_DE.UTF-8/en_US.UTF-8
## 
## time zone: Europe/Berlin
## tzcode source: internal
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## other attached packages:
##  [1] janitor_2.2.0      psych_2.4.12       semPlot_1.1.6      lavaan_0.6-19     
##  [5] magrittr_2.0.3     gt_0.11.1          knitr_1.49         DataExplorer_0.8.3
##  [9] lubridate_1.9.3    forcats_1.0.0      stringr_1.5.1      dplyr_1.1.4       
## [13] purrr_1.0.2        readr_2.1.5        tidyr_1.3.1        tibble_3.2.1      
## [17] ggplot2_3.5.1      tidyverse_2.0.0    here_1.0.1         see_0.10.0        
## [21] report_0.6.1       parameters_0.24.1  performance_0.13.0 modelbased_0.9.0  
## [25] insight_1.0.2      effectsize_1.0.0   datawizard_1.0.0   correlation_0.8.6 
## [29] bayestestR_0.15.2  easystats_0.7.4   
## 
## loaded via a namespace (and not attached):
##   [1] rstudioapi_0.17.1    jsonlite_1.8.8       estimability_1.5.1  
##   [4] farver_2.1.2         nloptr_2.1.1         rmarkdown_2.28      
##   [7] vctrs_0.6.5          minqa_1.2.8          base64enc_0.1-3     
##  [10] htmltools_0.5.8.1    haven_2.5.4          Formula_1.2-5       
##  [13] sass_0.4.9           bslib_0.8.0          htmlwidgets_1.6.4   
##  [16] plyr_1.8.9           emmeans_1.10.6       cachem_1.1.0        
##  [19] networkD3_0.4        igraph_2.0.3         lifecycle_1.0.4     
##  [22] pkgconfig_2.0.3      Matrix_1.7-0         R6_2.5.1            
##  [25] fastmap_1.2.0        snakecase_0.11.1     digest_0.6.37       
##  [28] OpenMx_2.21.13       fdrtool_1.2.18       colorspace_2.1-1    
##  [31] patchwork_1.3.0      rprojroot_2.0.4      Hmisc_5.2-3         
##  [34] labeling_0.4.3       timechange_0.3.0     abind_1.4-8         
##  [37] compiler_4.4.1       bit64_4.0.5          withr_3.0.2         
##  [40] glasso_1.11          htmlTable_2.4.3      backports_1.5.0     
##  [43] carData_3.0-5        MASS_7.3-60.2        GPArotation_2024.3-1
##  [46] corpcor_1.6.10       gtools_3.9.5         tools_4.4.1         
##  [49] pbivnorm_0.6.0       foreign_0.8-86       zip_2.3.1           
##  [52] nnet_7.3-19          glue_1.8.0           quadprog_1.5-8      
##  [55] nlme_3.1-164         lisrelToR_0.3        grid_4.4.1          
##  [58] checkmate_2.3.2      cluster_2.1.6        reshape2_1.4.4      
##  [61] generics_0.1.3       gtable_0.3.5         tzdb_0.4.0          
##  [64] data.table_1.16.4    hms_1.1.3            xml2_1.3.6          
##  [67] sem_3.1-16           pillar_1.10.1        vroom_1.6.5         
##  [70] rockchalk_1.8.157    splines_4.4.1        lattice_0.22-6      
##  [73] bit_4.0.5            kutils_1.73          tidyselect_1.2.1    
##  [76] pbapply_1.7-2        gridExtra_2.3        stats4_4.4.1        
##  [79] xfun_0.49            qgraph_1.9.8         arm_1.14-4          
##  [82] stringi_1.8.4        yaml_2.3.10          boot_1.3-30         
##  [85] evaluate_1.0.3       codetools_0.2-20     mi_1.1              
##  [88] cli_3.6.3            RcppParallel_5.1.9   rpart_4.1.23        
##  [91] xtable_1.8-4         munsell_0.5.1        jquerylib_0.1.4     
##  [94] Rcpp_1.0.14          coda_0.19-4.1        png_0.1-8           
##  [97] XML_3.99-0.18        parallel_4.4.1       jpeg_0.1-10         
## [100] lme4_1.1-35.5        mvtnorm_1.3-1        scales_1.3.0        
## [103] crayon_1.5.3         openxlsx_4.2.8       rlang_1.1.4         
## [106] mnormt_2.1.1

FFA-Norm values

Based on the 2009 Paper by Kohls, Sauer and Walach

Sebastian Sauer

2025-05-05 21:58:36.773452

1 Summary

2 Setup

3 Data

3.1 Prepare data

3.2 Item labels

3.3 Matching items to factors

4 Describe factors

4.1 Visualization of factor distributions

4.2 Descriptive statistics

4.3 Norms

5 Item statistics and reliability

5.1 FMI14

5.2 FMI13-R

6 CFA

6.1 Setup

6.1.1 Tetrachoric correlation matrix

6.2 One general mindfulness factor, including item 13

6.2.1 items as categorical, Pearson

6.2.2 items as categorical, Polychoric

6.2.3 items as numerical

6.2.4 items as categorical, Polychoric, mindfulness practitioners only

6.3 Two factors (presence, acceptance) without item 13, correlated factors

6.3.1 items as numeric:

6.3.2 items as categorical, Pearson

6.3.3 items as categorical, Polychoric

6.3.4 Plot

6.4 Two correlated factors, individuals with meditation practice only

6.4.1 items as numeric

6.4.2 items as categorical, Pearson

6.4.3 items as categorical, polychoric

6.5 Results

7 Norm values for different subgroups

7.1 Split by sex

7.1.1 Stats

7.1.2 Norms

7.2 Split by continuous mindfulness training

7.2.1 Stats

7.2.2 Norms

7.3 Split by retreats

7.3.1 Stats

7.3.2 Norms

7.4 Split by Vipassana continuously

7.4.1 Stats

7.4.2 Norms

7.5 Split by Age

7.5.1 Stats

7.5.2 Norms

8 Overview on descriptive statistics per subgroup

8.1 Regression models

8.1.1 m1

9 Session info